Syllabus for
MSc (Physics)
Academic Year  (2024)

Continuous internal assessment (CIA) forms 50% and the end semester examination forms the other 50% of the marks in both theory and practical. For the Holistic and Seminar course, there is no end semester examination and hence the mark is awarded through CIA. CIA marks are awarded based on their performance in assignments (written material to be submitted and valued), mid-semester examination (MSE), and class assignments (quiz, presentations, problem solving, etc.). The mid-semester examination and the end semester examination for each theory paper will be for two- and three-hours duration respectively. The CIA for practical sessions is done on a day-to-day basis depending on their performance in the pre-lab, the conduct of the experiment, and presentation of lab reports. Only those students who qualify with minimum required attendance and CIA marks will be allowed to appear for the end semester examination. 

The Department of Physics and Electronics CHRIST (Deemed to be University), Bengaluru was established in 1969, initiating BSc course with Physics, Chemistry and Mathematics (PCM) combination and subsequently Physics, Mathematics and Electronics (PME) combination in the year 1986. The department traces its roots as a postgraduate center affiliated to Bangalore University in 1993 with molecular and crystal physics as specialization. Under the autonomous institution system, the department has been offering MSc specialization in electronics and materials science since 2007.  MPhil and PhD programs were initiated under the “Deemed to be University” status, in 2008. Over the years, the department has become one of the best centers for quality higher education offered at the postgraduate and research levels. Research has been activated in the concerned subject areas both on campus and in collaboration with researchers at other institutions. The faculty members of the department carry out research in many frontier areas, which includes crystallography, superconductivity, nano-materials, nuclear physics and astrophysics. Faculty members and students have been recognized by national/international institutions in terms of awards and fellowships. The department has undertaken minor and major research projects supported by funding agencies such as UGC, DST, ISRO and Centre for Research, CHRIST (Deemed to be University).

The UG/PG program is designed to prepare students for teaching, higher research studies, or advanced scientific work in industry. Several research papers have been published in various national & international journals of repute apart from presentations across the globe. The department has also been actively organizing guest lecturers, national/regional conferences, workshops, refresher courses, seminars, and symposia to promote research and development activities.

Vision

Excellence and Service

Mission

To instil scientific temper and intellectual vigour among students, for contributing to the needs of society, by providing an environment of learning and knowledge creation through academic accompaniment.

The postgraduate program in physics helps to provide in-depth knowledge of the subject which is supplemented with tutorials, brainstorming ideas and problem-solving efforts pertaining to each theory and practical course. The two-year MSc program offers 16 theory papers and 7 laboratory modules, in addition to the foundation courses and guided project spreading over four semesters. Foundation courses and seminars are introduced to help the students to achieve holistic development and to prepare themselves to face the world outside in a dignified manner. Study tour to reputed national laboratories, research institutions, and industries, under the supervision of the department is part of the curriculum.

Programme Outcome/Programme Learning Goals/Programme Learning Outcome:

PO2: Develop critical thinking with a scientific temper and enhance problem-solving, analytical, and logical skills.

PO3: Communicate the subject effectively.

PO4: Understand the professional, ethical, and social responsibilities.

PO5: Enhance the research culture and uphold scientific integrity and objectivity.

PO6: Engage in continuous reflective learning in the context of technological and scientific advancements

PO7: To develop entrepreneurship skills through technically enhanced research environments.

Programme Specific Outcome:

PSO2: ● Understanding the basic concepts of physics, particularly concepts in classical mechanics, quantum mechanics, electrodynamics, and electronics, to appreciate how diverse phenomena observed in nature follow fundamental physical principles.

PSO3: Design and perform experiments in basic as well as advanced areas of physics.

PSO4: Develop proficiency in oral and written communication skills

Programme Educational Objective:

The course enables students to understand the basic concepts of Newtonian mechanics and introduce other formulations (Lagrange, Hamilton, Poisson) to solve trivial problems.  The course also includes constraints, rotating frames, central force, Kepler problems, canonical transformation and their generating functions, small oscillations and rigid body dynamics.

Mechanics of a particle, mechanics of a system of particles, constraints and their classification, principle of virtual work, D’Alembert’s principle, Generalized co-ordinates, Lagrange’s equations of motion, applications of Lagrangian formulation (simple pendulum, Atwood’s machine, bead sliding in a wire), cyclic co-ordinates, concept of symmetry, homogeneity and isotropy, invariance under Galilean transformations.

Rotating frames, inertial forces in the rotating frame, effects of Coriolis force, Foucault’s pendulum, Central force: definition and examples, Two-body central force problem, classification of orbits, stability of circular orbits, condition for closure of orbits, Kepler’s laws, Virial theorem, applications.                                                       

Canonical transformations, generating functions, conditions of canonical transformation, examples, Legendre’s dual transformation, Hamilton’s function, Hamilton’s equation of motion, properties of Hamiltonian and Hamilton’s equations of motion, Poisson Brackets, properties of Poisson bracket, elementary PB’s, Poisson’s theorem, Jacobi-Poisson theorem on PBs, Invariance of PB under canonical transformations, PBs involving angular momentum, principle of Least action, Hamilton’s principle, derivation of Hamilton’s equations of motion from Hamilton’s principle, Hamilton-Jacobi equation. Solution of simple harmonic oscillator by Hamilton-Jacobi method.

Types of equilibrium and the potential at equilibrium, Lagrange’s equations for small oscillations using generalized coordinates, normal modes, vibrations of carbon dioxide molecule, forced and damped oscillations, resonance, degrees of freedom of a free rigid body, angular momentum, Euler’s equation of motion for rigid body, time variation of rotational kinetic energy, Rotation of a free rigid body, Eulerian angles, Motion of a heavy symmetric top rotating about a fixed point in the body under the action of gravity.

[2].  Aruldhas, G. (2008). Classical mechanics : Prentice Hall India Learning Private Limited

[3].    Rana, N. C., & Joag, P. S. (1994).  Classical mechanics. New Delhi: Tata McGraw Hill.

[1].    Greiner, W. (2004). Classical mechanics: System of particles and Hamiltonian dynamics. New York: Springer-Verlag.

[2].    Barger, V., & Olsson, M. (1995). Classical mechanics - A modern perspective (2^nd ed.): Tata McGraw Hill.

[3].    Gupta, K. C. (1988). Classical mechanics of particles and rigid bodies: Wiley Eastern Ltd. 

[4].    Takwale, R. G., & Puranik, P. S. (1983).  Introduction to classical mechanics. New Delhi: Tata McGraw Hill.

This module introduces the students to the applications of analog and digital integrated circuits. First part of the module deals with the operational amplifier, linear applications of op-amp., active filters, oscillators, non-linear applications of op-amp, timer and voltage regulators. The second part deals with digital circuits which expose the logic gates, encoders and decoders, flip-flops registers and counters. 

The ideal op-amp - characteristics of an op-amp., the ideal op-amp., Equivalent circuit of an op-amp., Voltage series feedback amplifier - voltage gain, input resistance and output resistance, Voltage follower. Voltage shunt feedback amplifier - virtual ground, voltage gain, input resistance   and output resistance, Current to voltage converter. Differential amplifier with one op-amp. voltage gain, input resistance.

Linear applications: AC amplifier, AC amplifier with single supply voltage, Summing amplifier, Inverting and non-inverting amplifier, Differential summing amplifier, Instrumentation amplifier using transducer bridge, The integrator, The differentiator.                                                                                                               

Active filters and oscillators: First order low pass filter, Second order low pass filter, First order high pass filter, Second order high pass filter, Phase shift Oscillator, Wien-bridge oscillator, Square wave generator.

Non-linear circuits: Comparator, Schmitt trigger, Digital to analog converter with weighted resistors and R-2R resistors, Positive and negative clippers, Small signal half wave rectifier, Positive and negative clampers.                                                         

Logic gates - basic gates - OR, AND, NOT, NOR gates, NAND gates, Boolean laws and theorems (Review only). Karnaugh map, Simplification of SOP equations, Simplification of POS equations, Exclusive OR gates.

Combinational circuits: Multiplexer, De-multiplexer, 1-16 decoder, BCD to decimal decoder, Seven segment decoder, Encoder, Half adder, Full adder                  

Flip flops: RS flip-flop, Clocked RS flip-flop, Edge triggered RS flip-flop, D flip-flop, JK flip-flop, JK master-slave flip-flop.

Registers: Serial input serial output shift register, Serial input parallel output shift register, Parallel input serial output shift register, Parallel input parallel output shift register, Ring counter.

Counters: Ripple counter, Decoding gates, Synchronous counter, Decade counter, Shift counter - Johnson counter. 

[2].      Leach, D. P., & Malvino, A. P. (2002). Digital principles and applications. New York: Tata McGraw Hill.  

[2].      Morris Mano, M. (2018). Digital logic and computer design: Pearson India.

[3].      Jain, R. P. (1997). Modern digital electronics. New York: Tata McGraw Hill.

Course Description:  This course being an essential component in understanding the behaviour of fundamental constituents of matter is divided into two modules spreading over the first and second semesters. The first module is intended to familiarize the students with the basics of quantum mechanics, exactly solvable eigenvalue problems, a general formulation of quantum mechanics - alternative approach, momentum space, generalized uncertainty relation, angular momentum - spin angular momentum, the addition of angular momentum, Clebsch-Gordan coefficients.

Course Objectives: Upon successful completion of this course the student will be able to: 

·       Employ the basic principles of quantum mechanics to wave functions to calculate the observables 

·       Solve time-dependent and time-independent Schrödinger equation for simple potentials 

·        Apply the Matrix formulation of quantum mechanics and introduce the Bra and Ket vectors

·        Describe the angular momenta and their properties

Review – Inadequacies of classical theory, development of quantum mechanics, Schrödinger equation, physical interpretation of wave functions, probability density, probability current density, orthogonality and normalization of the wave function. Superposition of plane waves: formulation of Schrödinger equation in momentum representation, Operator formalism in quantum mechanics, Hermitian operators, Analogy between Poisson brackets and commutators, Eigenvalues, Eigenfunctions, postulates of quantum mechanics, expectation values, Ehrenfest theorems.

Bound and unbound systems Potential step, rectangular potential barrier - reflection and transmission coefficient, barrier penetration-applications (alpha-decay) particle in a one-dimensional box and in a cubical box, one-dimensional linear harmonic oscillator - evaluation of expectation values of x²and p_x²; spherically symmetric systems: Rigid rotator, Hydrogen atom - solution of radial equation.

Linear transformations, eigenvalues; eigenvectors: characteristic equation of a matrix, theorems on eigenvalues and eigenvectors - eigenvectors of a set of commuting operators with and without degeneracy, complete set of commuting operators, Hilbert space, operators as matrices, matrix form of wavefunction, unitary transformation and its properties, Eigenvalue problems, Equation of motion: Schrödinger picture, Heisenberg picture and Interaction picture. Dirac’s bra and ket vectors: Dual space, Direct sum and product of Hilbert spaces, coordinate and momentum representation, parity and projection operators, Generalized uncertainty relation. Matrix theory of harmonic oscillator.

Angular momentum operator, rotational operator and angular momentum, spin and total angular momentum operators, commutation relations, ladder operators, eigenvalue spectrum of J²and J_z, and Pauli spin matrices and eigenvectors of spin half systems, matrix representation of J_x, J_y and J_z, J², addition of two angular momenta, Evaluation of Clebsch-Gordan coefficients, singlet and triplet states, recursion relations.

[1]. Zettili, N. (2017). Quantum mechanics. New Delhi: Wiley India Pvt Ltd.

[2]. Griffiths, D. J. (1995). Introduction to quantum mechanics: Prentice Hall Inc.

[3]. Aruldhas, G. (2010). Quantum mechanics. New Delhi: Prentice Hall of India.

[4]. Ghatak, A. K. & Lokanathan, S. (1997). Quantum mechanics: McMillan India Ltd

[5]. Satya Prakash (2009). Advanced Quantum Mechanics: (5th Edition) Kadar Nath Ram Nath.

[6]. Schiff, L. I. (2017). Quantum mechanics (4th ed.). New York: McGraw Hill Education Pvt Ltd.

[7]. Miller, D. A. B. (2008). Quantum mechanics for scientists and engineers: Cambridge

University Press.

[8]. Sakurai, J. J. (2002). Modern quantum mechanics: Pearson Education Asia.

[9]. Crasemann, B., & Powell, J. H. (1998). Quantum mechanics: Narosa Publishing House.

[10]. Mathews, P. M., & Venkatesan, A. (1995). Quantum mechanics. New Delhi: Tata

McGraw Hill.

[12]. Gasiorowicz, S. (1974). Quantum physics: John Wiley & Sons.

[13]. Landau, L. D., & Lifshitz, E. M. (1965). Quantum mechanics: Pergamon Press

[14]. Shankar, R. (2008). Principles of quantum mechanics (2nd ed.). New York: Springer.

[15]. Tamvakis, K. (2005). Problems and solutions in quantum mechanics: Cambridge

University Press.

A sound mathematical background is essential to understand and appreciate the principles of physics. This module is intended to make the students familiar with the applications of tensors and matrices, Special functions, partial differential equations and integral transformations, Green’s functions and integral equations.

Vectors and matrices: Review (vector algebra and vector calculus, gradient, divergence & curl), transformation of vectors, rotation of the coordinate axes, invariance of the scalar and vector products under rotations, Vector integration, Line, surface and volume integrals - Stoke’s, Gauss’s and Green’s theorems (Problems), Vector analysis in curved coordinate, special coordinate system - circular, cylindrical and spherical polar coordinates, linear algebra matrices, Cayley-Hamilton theorem, eigenvalues and eigenvectors.

Tensors: Definition of tensors, Kronecker delta, contravariant and covariant tensors, direct product, contraction, inner product, quotient rule, symmetric and antisymmetric tensors, metric tensor, Levi Cevita symbol, simple applications of tensors in non-relativistic physics.

Beta and Gamma functions, different forms of beta and gamma functions. Dirac delta function. Kronecker delta, Power series method for ordinary differential equations, Series solution for Legendre equation, Legendre polynomials and their properties, Series solution for Bessel equation, Bessel and Neumann functions and their properties, Series solution for Laguerre equation, it's solutions and properties (generating function, recurrence relations and orthogonality properties for all functions). 

Method of separation of variables, the wave equation, Laplace equation in cartesian, cylindrical and spherical polar coordinates, heat conduction equations and their solutions in one, two and three dimensions. 

Review of Fourier series, Fourier integrals, Fourier transform, Properties of Fourier sine and cosine transforms, applications. Laplace transformations, properties, convolution theorem, inverse Laplace transform, Evaluation of Laplace transforms and applications.

Dirac delta function, properties of Dirac delta function, three dimensional delta functions, boundary value problems, Sturm-Liouville differential operator, Green’s function of one dimensional problems, discontinuity in the derivative of Green’s functions, properties of Green’s functions, Construction of Green’s functions in special cases and solutions of inhomogeneous differential equations, Green’s function- symmetry of Green’s function, eigenfunction expansion of Green’s functions, Green’s function for Poisson equation.

Linear integral equations of first and second kind, Relationship between integral and differential equations, Solution of Fredholm and Volterra equations by Neumann series method. 

[2]. Dass, H. K. (2008). Mathematical physics. New Delhi: S. Chand and Sons.

[3]. Prakash, S. (2004). Mathematical physics. New Delhi: S. Chand and Sons.

[5]. Mathews, J., & Walker, R. (2006). Mathematical physics: Benjamin, Pearson Education.

[6]. Kryszig, E. (2005). Advanced engineering mathematics: John-Wiley.

[7]. Hassani, S. (2000). Mathematical methods for students of physics and related fields: Springer.

[8]. Joshi, A W. (1995). Tensor analysis: New Age International Publishers.

[9]. Chattopadhyaya, P. K. (1990). Mathematical physics: Wiley Eastern.

[10]. Boas, M. L. (1983). Mathematical methods in the physical sciences (2nd ed.): John-Wiley

[11]. Spiegel, M. R. (1974). Theory and problems of vector analysis (Schaum’s outline series):McGraw-Hill Publishing Co.

[12]. Piper, L. A. (1958): Applied mathematics for engineers and physicists. New York: McGraw-Hill.

CIA 1: Assignment /quiz/ group task / presentations before MST - 10 marks.

CIA 2: Mid-Sem Test (Centralized), 2 hours - 50 marks to be converted to 25 marks.

CIA 3: Assignment /quiz/ group task / presentations after MST - 10 marks.

CIA 4: Attendance (76-79 = 1, 80-84 = 2, 85-89 = 3, 90-94 = 4, 95-100 = 5) - maximum of 5 marks.

Experiments are selected to improve the understanding of students about mechanical, magnetic, optical and basic electronic properties of materils.

1. Elastic constants of glass plate by Cornu's interference method. 

2. Study of thermo-emf and verification of thermoelectric laws

3. Wavelength of iron arc spectral lines using constant deviation spectrometer. 

4. Energy gap of the semi-conducting material used in a PN junction. 

5. Characteristics of a solar cell.

6. Stefan’s constant of radiation.

7. Relaxation time constant of a serial bulb.

8. e/m by Millikan’s oil drop method.

9. Study of elliptically polarized light by using photovoltaic cell.                                      

10. Study of absorption of light in different liquid media using photovoltaic cell. 

11. Determination of Curie temperature of a given ferro magnetic material. 

12. Determination of energy loss during magnetization and demagnetization by means of BH loop.

1.      Elastic constants of glass plate by Cornu's interference method. (Online/Offline)

2.      Study of thermo-emf and verification of thermoelectric laws (Onlilne/Offline)

3.      Wavelength of iron arc spectral lines using constant deviation spectrometer. (Offline)

4.      Energy gap of the semi-conducting material used in a PN junction. (Offline)

5.      Characteristics of a solar cell. (Online/Offline) 

6.      Stefan’s constant of radiation. (Offline)

7.    Study of hydrogen spectra and determination of Rydberg constant (Offline)

1.      Relaxation time constant of a serial bulb. (Offline)

2.      e/m by Millikan’s oil drop method. (Online)

3.      Study of elliptically polarized light by using photovoltaic cell. (Offline)                                     

4.      Study of absorption of light in different liquid media using photovoltaic cell. (Offline/Online)

5.      Determination of Curie temperature of a given ferro magnetic material. (Offline)

6.      Determination of energy loss during magnetization and demagnetization by means of BH loop. (Online/Offline)

2. Sears, F. W., Zemansky, M. W.,& Young, H. D. (1998). University physics(6^thed.): Narosa Publishing House.

4. Collings, P. J. (1980). Simple measurement of the band gap in silicon and germanium, Am. J. Phys., Vol. 48, Page. 197.

5. Fischer, C. W. (1982). Elementary technique to measure the energy band gap and diffusion potential of pn junctions: Am. J. Phys., Vol. 50, Page. 1103.

Electronics being an integral part of Physics, electronics lab is dedicated to experiments related to electronic components and circuits. The experiments are selected to application in electronic circuits. During the course, the students will get to know the use of various electronic measuring instruments for the measurement of various parameters.

1. Transistor multivibrator.
2. Half wave and full wave rectifier using op-amp.
3. Op-amp. voltage regulator.
4. Op-amp. inverting and non-inverting amplifier.
5. Timer 555, square wave generator and timer.
a) RS flip-flop using NAND gates, b) Decade counter using JK flip-flops.

6. Half adder and full adder using NAND gates.
7. Construction of adder, subtractor, differentiator and integrator circuits using the given Op-amp.
8. Construction of a D/A converter circuit and study its performance-R-2R and Weighted resistor network.
9. JK Flip-Flop and up-down counter
10. Differential Amplifier with Op-Amp

11. Low-pass, high-pass and band-pass filters (first order - active filters)

12. Multiplexer and demultiplexer-( IC 74151, IC74138)

13. Encoder and priority encoder- (IC74148 and IC74147)

14. Decoder and seven segment display- (IC 74LX138 and IC7447)

 Course description: The research methodology module is intended to assist students in planning and carrying out research projects. The students are exposed to the principles, procedures and techniques of implementing a research project. In this module the students are exposed to elementary scientific methods, design and execution of experiments, analysis and reporting of experimental data. Units I and II caters to local and national needs.

Course Outcomes: This course enables the students to 

● Understand the basic concept of research methodology 

● Differentiate between research methods and methodology 

● Understand different stages of research methodology 

● Write reports/documents/articles/presentations in Latex 

 Introduction - meaning of research - objectives of research - motivation in research, types of research - research approaches - significance of research -research methods versus methodology - research and scientific method, importance of knowing how research is done - research processes - criteria of good research - defining research problem - selecting the problem, necessity of defining the problem - techniques involved in defining a problem - research design - meaning of research design - need for research design - features of good design, different research designs - basic principles of experimental design. Resources for research - research skills - time management, role of supervisor and scholar - interaction with subject experts. Thesis Writing: The preliminary pages and the introduction - the literature review, methodology - the data analysis - the conclusions, the references (IEEE format)

 Literature review: Significance of review of literature - source for literature: books -journals - proceedings - thesis and dissertations - unpublished items.

On-line Searching: Database – SciFinder – Scopus - Science Direct - Searching research articles - Citation index - Impact factor - h-index etc.

Document preparation system: Latex, beamer, Overleaf - Writing scientific report - structure and components of research report - revision and refining’ - writing project proposal - paper writing for international journals, submitting to editors - conference presentation - preparation of effective slides, graphs - citation styles.

[2].Panneerselvam, R. (2005). Research methodology. New Delhi: PHI.

[4].Kumar, R. (2005). Research methodology: A step by step guide for beginners (2nd ed.): SAGE Publications Ltd.

[5].Gregory, I. (2005). Ethics in research:Bloomsbury Publishing PLC.

[6].Nakra, B. C., & Chaudhry, K. K. (2005). Instrumentation, measurement and analysis (2nd ed.). New Delhi: TMH Publishing Co. Ltd.

[7].     Oliver, P. (2004). Writing your thesis. New Delhi: Vistaar Publications.

[8].     Mittelbach, F., & Goossens, M. (2004), The LATEX Companion: Addison-Wesley Professional.

This course develops basic concepts of statistical mechanics, statistical interpretation of thermodynamics and various ensembles. The course also introduces various methods used in statistical mechanics to study Bose-Einstein and Fermi-Dirac systems. Numerous examples illustrating a wide variety of physical phenomena such as magnetism, polyatomic gases, superfluidity, electrons in solids, and phase transitions are discussed.

Introduction, phase space, ensembles (microcanonical, canonical and grand canonical ensembles), ensemble average, Liouville theorem, conservation of extension in phase space, condition for statistical equilibrium, microcanonical ensemble, ideal gas.

Quantum picture: Microcanonical ensemble, quantization of phase space, basic postulates, classical limit, symmetry of wave functions, effect of symmetry on counting, distribution laws.

Gibb’s paradox and its resolution, Canonical ensemble, entropy of a system in contact with a heat reservoir, ideal gas in canonical ensemble, Maxwell velocity distribution, equipartition theorem of energy, Grand canonical ensemble, ideal gas in grand canonical ensemble, comparison of various ensembles.

Canonical partition function, molecular partition function, translational partition function, rotational partition function, application of rotational partition function, application of vibrational partition function to solids.

Bose-Einstein distribution, Applications, Bose-Einstein condensation, thermodynamic properties of an ideal Bose-Einstein gas, liquid helium, two fluid model of liquid helium-II, Fermi-Dirac (FD) distribution, degeneracy, electrons in metals, thermionic emission, magnetic susceptibility of free electrons. Application to white dwarfs, high temperature limits of BE and FD statistics.

First order and second order phase transitions: Phase diagrams, phase equilibria and phase transitions, Order parameter, Critical exponents. 1D Ising model, Elementary ideas on Ising and Heisenberg models of ferromagnetism. Diffusion  equation: random  walk  and  Brownian  motion; introduction to non-equilibrium processes, Boltzmann transport equation. 

[4].    Salinas, R. A. (2006). Introduction to statistical physics: Springer.

[5].    Bhattacharjee, J. K., (1997). Statistical physics: Equilibrium and mon-equilibrium aspects: Allied Publishers Ltd.

[6].    Huang, K. (1991). Statistical mechanics: Wiley Eastern Limited.

[7].    Reif, F. (1985). Statistical and thermal physics: McGraw Hill International.

[8].    Gopal, E. S. R. (1976). Statistical mechanics and properties of matter: Macmillan.

This course has been conceptualized in order to give students to get exposure to the fundamentals of Electrodynamics. Students will be introduced to the topics such as Electrostatics, Magnetostatics, Electromagnetic waves, Propagation of wave through waveguide, Electromagnetic radiation and relativistic electrodynamics. 

Electrostatics:Review of electrostatics, Electrostatic boundary conditions, Poisson’s equation and Laplace’s equation, uniqueness theorem.  Solution to Laplace’s equation in a) Cartesian coordinates, applications: i) rectangular box and ii) parallel plate condenser, b) spherical coordinates, applications: potential outside a charged conducting sphere and c) cylindrical coordinates, applications: potential between two co-axial charged conducting cylinders. Method of images: Potential and field due to a point charge i) near an infinite conducting sphere and ii) in front of a grounded conducting sphere.

Magnetostatics: Review of magnetostatics, Multipole expansion of the vector potential, diamagnets, paramagnets and ferromagnets, magnetic field inside matter, Ampere’s law in magnetized materials, Magnetic susceptibility and permeability.

Review of Maxwell’s equations, Maxwell’s equations in matter, Boundary conditions. Poynting’s theorem, wave equation, Electromagnetic waves in vacuum, energy and momentum in electromagnetic waves. Electromagnetic waves in matter, Reflection and transmission at normal incidence, Reflection and transmission at oblique incidence. Electromagnetic waves in conductors, reflection at a conducting surface, and frequency dependence of permittivity.     

Waveguides - Rectangular wave guides (uncoupled equations), TE mode, TM mode, wave propagation in the guide, wave guide resonators-TM mode to z, TE mode for z. Potential formulation - Scalar and vector potentials, Gauge transformations, Coulomb and Lorentz gauge, retarded potentials, Lienard-Wiechert potentials, the electric and magnetic fields of a moving point charge.

Electric dipole radiation, magnetic dipole radiation, Power radiated by a point charge, radiation reaction, mechanism responsible for radiation reaction.         

Relativistic electrodynamics: Review of Lorentz transformations. Magnetism as a relativistic Phenomenon, Transformation of electric and magnetic Fields, Electric field of a point charge in uniform motion, Field tensor, Electrodynamics in tensor notation, Relativistic potentials.

[1].Sadiku, M. N. O. (2010). Elements of electromagnetics (4^th ed.): Oxford Press.

[2].Griffiths, D. J. (2002). Introduction to electrodynamics: Prentice-Hall of India.

[1].Panofsk, W. K. H., & Phillips, M. (2012). Classical electricity and magnetism (2^nd ed.). New York, NY: Dover Publishing Inc.

[2].Jackson, J. D. (2007). Classical electrodynamics (3^rd ed.). New York, NY: Wiley India Pvt. Ltd.

[3].Singh, R. N. (1991). Electromagnetic waves and fields. New York, NY: Tata McGraw Hill.

[4].Lorrain, P., & Corson, D. (1986): Electromagnetic fields and waves. New Delhi: CBS Publishers and Distributors.

Course Description: This module is a continuation of the course on Quantum Mechanics-I, introduced in the first semester. In this module the students will be introduced to symmetry and identical particles - origin of conservation laws, time-independent perturbation theory and time-dependent perturbation theory, scattering theory, relativistic quantum mechanics - inclusion of relativistic effects into quantum realm and quantisation of fields.

Translational symmetry in space and conservation of linear momentum, translational symmetry

in time and conservation of energy, Rotational symmetry and conservation of angular momentum, symmetry and degeneracy, parity (space inversion) symmetry, even and odd parity.

Identical particles, symmetric and antisymmetric wave functions, construction of symmetric and antisymmetric wave functions from unsymmetrised functions, distinguishability of identical particles, the Pauli exclusion principle, spin: Pauli’s spin matrices for electron, commutation relations satisfied by three components σ_x, σ_y and σ_z, two-component wavefunctions.

Time independent perturbation theory- First and second-order perturbation theory applied to non-degenerate case; first-order perturbation theory for degenerate case, application to normal

Zeeman effect and Stark effect in hydrogen atom. The variation method, application to ground state of Helium atom.

Time-dependent perturbation theory - First order perturbation, Harmonic perturbation, Fermi’s golden rule, application to semi-classical theory of radiation, Adiabatic approximation, Sudden approximation.

Scattering cross-section, Differential and total cross-sections, Born approximation for the scattering amplitude, validity, scattering by spherically symmetric potentials, screened coulomb potential, Partial wave analysis for scattering amplitude, expansion of a plane wave into partial waves, phase shift, cross-section expansion, s-wave scattering by a square well, optical theorem, matrix formulation of scattering under central filed.

Klein-Gordon equation for a free particle and its applications, Dirac relativistic equation for a free particle, Dirac matrices, orthonormality and completeness of free particle solutions, existence of electron spin.

Quantisation of Fields: The classical approach to field theory, relativistic Lagrangian and Hamiltonian of a charged particle in em field, the Lagrangian and Hamiltonian formulations, quantum equation for the field.

[1]. Zettili, N. (2017). Quantum mechanics. New Delhi: Wiley India Pvt Ltd.

[2]. Griffiths, D. J. (1995). Introduction to quantum mechanics: Prentice Hall Inc.

[3]. Satya Prakash (2009). Advanced Quantum Mechanics: (5th Edition) Kadar Nath Ram Nath.

[4]. Aruldhas G. (2010). Quantum Mechanics, New Delhi: Prentice Hall of India.

[5]. Dirac P. A. M. (1967). The Principles of Quantum Mechanics (4th ed.), London: Oxford University Press.

[6]. Schiff L. I. (2017). Quantum Mechanics (4th ed.), New York: McGraw Hill Education Pvt Ltd.

[7]. Mathews P. M. and Venkatesan A. (1995). Quantum Mechanics, New Delhi: TMH Publishers.

[8]. Miller D. A. B. (2008). Quantum Mechanics for Scientists and Engineers, England: Cambridge University Press.

[9]. Feynman R. P., Leighton R. B. and Sands (1966). The Feynman Lecture on Physics, Vol. 3: Addison-Wesley Publishing Company, Inc.

[10]. Tamvakis K. (2005). Problems and Solutions in Quantum Mechanics, England: Cambridge University Press.

[11]. Gasiorowicz S. (1974). Quantum Physics, New Jersey, USA: John Wiley & Sons.

[12]. Sakurai J. J. (2002). Modern Quantum Mechanics, New York: Pearson Education Asia.

CIA 1: Assignment /quiz/ group task / presentations before MSE - 10 marks.

CIA 2: Mid-Sem Eest (Centralized), 2 hours - 50 marks to be converted to 25 marks.

CIA 3: Assignment /quiz/ group task / presentations after MST - 10 marks.

CIA 4: Attendance (76 - 79 = 1, 80 - 84 = 2, 85 - 89 = 3, 90 - 94 = 4, 95 - 100 = 5) - maximum of 5 marks.

Course description: A sound mathematical background is essential to understand and appreciate the principles of physics. This module is intended to make the students familiar with the applications of complex analysis, probability theory and group theory. Also, the students will get a complete understanding of different numerical techniques.

Course Objectives: On completion of the course, the student will be able to

● Solve problems in complex analysis including the integral theorems, residue theorem etc.

Introduction, Analytic functions, Cauchy-Reimann conditions, Cauchy's integral theorem and integral formula, Taylor and Laurent expansion- poles, residue and residue theorem, classification of singularities, Cauchy's principle value theorem, evaluation of integrals, applications.

Elementary probability theory, Random variables, Binomial, Poisson and Gaussian distributions-central limit theorem.

Basic definitions and concepts of group - point, cyclic groups,  Multiplication table, Subgroups, Cosets and Classes, Permutation Groups, Homomorphism and isomorphism, Reducible and irreducible representations, Schur’s lemmas and great orthogonality theorem, Elementary ideas of Continuous groups - Lie, rotation, unitary groups- GL(n), SO(3), SU(2), SO(3,1), SL(2,C).

Direct solutions of Linear equations: Solution by elimination method, Basic Gauss elimination method, Gauss elimination by pivoting. Matrix inversion method, Iterative solutions of linear equations: Jacobi iteration method, Gauss Seidel method. Roots of nonlinear equations: Bisection method, Newton-Raphson method. Curve fitting by regression method: Fitting linear equations by least squares method, fitting transcendental   equations, fitting a polynomial function.                                                                                                                                                                                                                                                                           

Numerical integration: Trapezoidal Rule, Simpson’s 1/3 rule and Simpsons 3/8 rule. Numerical solution of ordinary differential equations: Euler’s method, Runge-Kutta method (2nd order and 4th order methods). 

Freely falling body, motion of a projectile, simple harmonic motion, motion of charged particle in an electric field, motion of charged particle in a uniform magnetic field, solution of time independent Schrodinger equation.

2. Dass, T., & Sharma, S. K. (2009). Mathematical methods in classical and quantum physics: Universities Press.

3. Balaguruswamy, E. (2002). Numerical methods. New Delhi: Tata McGraw Hill.

1. Gupta, B.D. (2009). Mathematical physics. New Delhi: Vikas Publication House. 

2. Prakash, S. (2004). Mathematical physics: S. Chand and Sons.

3. Rajaraman, V. (2002). Computer oriented numerical methods (3rd ed.). New Delhi: Prentice Hall of India Pvt Ltd.

4. Joshi, A.W. (1997). Elements of group theory for physicists: New Age International.

5. Sastry, S. S.  (1995). Introductory methods of numerical analysis (2nd ed.). New Delhi: Prentice Hall of India Pvt. Ltd.

6. Baumslag, B., & Chandler, B. (1968). Group theory - Schaum’s series: McGraw-Hill Education.

This course contains the experiments which are intended to improve the understanding of students about Dielectric, magnetic, optical (absorption characteristics) and basic electronic properties of materials.

1. Wavelength of LASER light by interference and diffraction method.

2. Thickness of mica sheet by optical method (Edser-Butler method).

3. Velocity of ultrasonic waves in liquid media (Kerosene & CCl4).

4. Study of polarized light using Babinet's compensator.

5. Thermal expansion of a solid by optical interference method.

6. Hartmann's constants and study of electronic absorption band of KMnO4.

7. Wavelength of Laser source and thickness of glass plate using Michelson Interferometer.

8. Coefficient of thermal and electrical conductivity of copper and hence to determine Lorentz number.

9. Dielectric constant of benzene and CCl4 molecules.

10. (a) Size of lycopodium particles by diffraction method. (b) Refractive index of transparent material and a given liquid

11. Determination of thickness of thin film using Swanepeol method (Envelop method).

1.      Wavelength of LASER light by interference and diffraction method. (Online/Offline)

2.      Thickness of mica sheet by optical method (Edser-Butler method). (Offline)

3.      Velocity of ultrasonic waves in liquid media (Kerosene & CCl₄).

4.      Study of polarized light using Babinet's compensator.

5.      Thermal expansion of a solid by optical interference method. (Offline)

 1.      Hartmann's constants and study of electronic absorption band of KMnO₄. (Offline)

 2.      Wavelength of Laser source and thickness of glass plate using Michelson Interferometer. (Online/Offline)

 3.      Coefficient of thermal and electrical conductivity of copper and hence to determineLorentz number. (Online)

 4.      Dielectric constant of benzene and CCl₄ molecules. (Offline/Offline)

 5.      (a) Size of lycopodium particles by diffraction method.(b) Refractive index of transparent material and a given liquid (Offline)

[1].   B. L. Worsnop and H. T. Flint: Advanced Practical Physics for students, Asia Publishing house, New Delhi 1984.

[1].   F. W. Sears, M. W. Zemansky and H. D. Young : University Physics, 6^th Edn., Narosa publishing house, 1998

[2].   M. S. Chauhan and S. P. Singh: Advanced practical physics, Pragati Prakashan, Meerut.

[3].   S. Chadda and S. P. Mallikarjun Rao: Determination of Ultrasonic Velocity in Liquids Using Optical Diffraction By Short Acoustic Pulses, Am. J. Phys. 47, 464 (1979).

Course description: This module makes the students familiar with the use of computers for applications in Physics. The first few sessions will be used to make the students familiar with the basics of python programming. It is followed by about ten experiments in solving problems using numerical techniques. It is then followed by a few experiments to get the students familiar with the problems and principles of physics.

Course Objectives:On completion of this course the student will be able to

● Design object oriented code in the open source Python programming language.

● Develop the skill of devising graphical user interfaces in Python

● Employ the knowledge in programming to numerical problems they encounter in experimental and theoretical research projects.

1. Generate an online calculator, sum of ’n’ number and factorial of a number 

2. Generate the Fibonacci series, check whether the number is prime or not and print the prime numbers in a range of values

3. User defined matrix addition and multiplication, determine the determinant of a matrix.

4. Construct a logic gate simulator and solve the logic gate circuit.

5. Familiarisation with histogram, scatter and curve plotting techniques.

6. Solution of linear equations using Gauss elimination method

7. Iterative solutions of linear equations using Jacobi iteration method and Gauss Seidel method.

8. Roots of non linear equations using bisection method and Newton-Raphson method.

9. Linear fitting by regression method.

10. Numerical integration of a function using Trapezoidal rule and Simpson’s rules.

11. Euler's method and Runge-Kutta method to obtain the numerical differential of a function.

12. Linear regression - Least squares method to fit a straight line.

13. Problem of free fall using Runge-Kutta method.

14. Simple harmonic motion of a loaded spring using Euler’s method.

2. E. Balaguruswamy: Numerical Methods, TMH, New Delhi, 2002

3. Harsh Bhasin, Python for Beginners, New Age International (P) Ltd, 2019

 The research techniques and tools program is intended to equip students with the necessary software and data analysis knowledge in carrying out research projects. The students are exposed to the principles, procedures and techniques of implementing a research project. In this module the students are exposed to elementary scientific methods, various data analysis techniques, plotting routines etc.

Introduction to data analysis - least-squares fitting of linear data and non-linear data - exponential type data - logarithmic type data - power function data and polynomials of different orders. Fitting of linear, Non-linear, Gaussian, Polynomial, and Sigmoidal type data - Fitting of exponential growth, exponential decay type data - plotting polar graphs - plotting histograms - Y error bars - XY error bars - data masking. Review of Plotting (Python/Excel/Origin).

Quantitative techniques (Error Analysis) - General steps required for quantitative analysis - reliability of the data -classification of errors–accuracy–precision-statistical treatment of random errors-the standard deviation of complete results - error proportion in arithmetic calculations - uncertainty and its use in representing significant digits of results - confidence limits - estimation of the detection limit.

Understanding the need, basic guidelines, content and process for Value Education, Right understanding of self, happiness, respect, integrity, relationships, etc. Understanding the harmony in self, family and professional areas, Understanding and living in harmony at various levels. 

Ethics -Definitional aspects; relevance of ethics in society, The philosophical basis of ethics, considerations on moral philosophy- personal and family ethics, fundamental values in professionals such as dispassion, moral integrity, objectivity, dedication to public service and empathy for weaker sections and non-corruptibility, Ethics at the workplace- cybercrime, plagiarism, sexual misconduct, fraudulent use of institutional resources, etc.

1. C. R. Kothari, Research Methodology Methods and Techniques, 2nd. ed. New Delhi: New Age International Publishers, 2009.

2. R. Panneerselvam, Research Methodology, New Delhi: PHI, 2005.

3. P. Oliver, Writing Your Thesis, New Delhi: Vistaar Publications, 2004.

Course description: This course has been conceptualised in order to give students an exposure to the fundamentals of nuclear and particle physics. Students will be introduced to the new ideas such as the properties and structure of nucleus, different theoretical approaches to the structure of nucleus, nuclear force, beta decay, neutrino hypothesis, Fermi’s theory, interaction of nuclear radiations with matter and the principles behind the working of radiation detectors, fundamental particles and their interactions, particle accelerators. Unit III caters to national and global needs.

Course objectives:

• To understand the underlying structure of nucleus, properties, how the nuclear radiations interact with matter and form the basis for the working of nuclear radiation detectors. 
• To apply different models to understand the structure and properties of nucleus
• To analyse the interaction of radiation with matter, determine the unknown radioactive sources using NaI(Tl) detector.

Review on semi-empirical mass formula (Bethe-Weizsacker formula), stability of nuclei against beta decay, mass parabola, end point energy of beta particles and radius parameter for mirror nuclei. Fermi gas model - kinetic energy for the ground state, asymmetry energy. Nuclear shell model - magic numbers and evidences, prediction of energy levels in an infinite square well potential, spin-orbit interaction potential (extreme single particle shell model), prediction of spin, parity and magnetic moment of odd A nuclei, Schmidt diagrams, Nordheim’s rule for the prediction of spin and parity of odd Z-odd N nuclei.

Nuclear force: Characteristics of nuclear force, short range, saturation, charge independent, spin dependent, exchange characteristics, ground state of the deuteron using square well potential, relation between the range and depth of the potential, Yukawa theory of exchange nature of nuclear force (qualitative only). 

Nuclear decay: Beta decay - Q value of beta decay, nonconservation of energy and angular momentum in beta decay, neutrino hypothesis, Fermi’s theory of beta decay, Kurie’s plots and ‘ft’ values, selection rules, detection of neutrino, nonconservation of parity in beta decay, experimental proof. Gamma decay - energetics of gamma decay, selection rules, multipolarity, internal conversion process (qualitative).

Types of nuclear reactions, conservation laws, cross section, differential cross section, energetics of nuclear reactions, threshold energy, direct and compound nuclear reactions, their mechanisms, Bohr’s independence hypothesis, Goshal experiment. Nuclear fusion and fission: Energy released in fusion and fission, neutron multiplication and chain reaction in thermal reactor, four factor formula, reactor and its components.

Interaction of radiation with matter:Interaction of charged particles with matter - energy loss of heavy charged particles in matter, Bethe-Bloch formula. Energy loss of electrons and beta particles, absorption coefficient for beta rays. Interaction of gamma rays with matter - Photoelectric, Compton and Pair production, Coherent scattering (Rayleigh and Thomson), total interaction cross-section and mass attenuation coefficient for gamma rays, scintillation detector, Scintillation mechanism in NaI(Tl), NaI(Tl) gamma ray spectrometer. Semiconductor radiation detectors - surface barrier detectors, Li ion drifted detectors (Si(Li) and Ge(Li)).

Elementary particles: Elementary particles and their properties, Fundamental interactions in nature, classification based on type of interaction, conservation laws, symmetry classification of elementary particles (SU2 and SU3 symmetry). Quark hypothesis, quark structures of mesons and baryons, quantum chromodynamics.

M. Thomson: Modern Particle Physics, Cambridge University Press, 2013.

D. H. Frisch and A. M. Thorndike: Elementary Particles, D. Van Nostrand, 1964.

K. S. Krane: Introductory Nuclear Physics, Wiley, 2003.

R. R. Roy and B. P. Nigam: Nuclear Physics, Wiley Eastern Ltd., 1967. 

S. S. Kapoor and V. S. Ramamoorthy: Radiation Detectors, Wiley Eastern, 1986.

G. F. Knoll: Radiation Detection and Measurement, 2nd Edn. John Wiley, 1989.

 CCIA I - 20 marks (Research Based Assessment, Submission type assignment).

     CIA II - 20 marks (Descriptive type test and problem solving, Submission type).

     CIA III - 20 marks (Experiential learning, Submission type).

     ESE - 50 marks (Descriptive/Problem solving, Written type, finally converted to 40 marks).

Course description: This course covers the fundamentals of the physics of solids. We will explore how the properties of solids are determined by microscopic physics. The course focuses on structural and electronic properties, dielectrics and ferroelectric, magnetic and superconducting properties of solids. 

Course Objective: This course will investigate the structural and physical properties of materials by developing a better understanding of crystal structure with particular emphasis on studying the electrical and magnetic behavior of solids. The course shows how various types of phenomena (optical, electrical, magnetic, superconductivity) are related. The main objectives of the course are to increase the students understanding and knowledge of solid-state physics and to improve their problem-solving ability, including the design of experiments which examine principles in condensed matter physics.

Crystal structure: Review of crystalline state, Bravais lattice, Reciprocal lattice, Fourier expansion of lattice periodic functions (meaning of reciprocal lattice), General theory of X-ray diffraction, Ewald construction, Relation between Bragg and Laue theory.

Lattice dynamics: Elastic versus lattices waves, Vibrations in an infinite chain of atoms with one and two atoms per unit cell, Dispersion relations, Brillouin Zones, Group and phase velocities, Quantized vibrations, phonons, Density of states, Debye theory of specific heat, anharmonicity and thermal expansion.

Drude’s model, Sommerfeld model, Explanation of hall-effect, Failure of free electron model. Energy bands in solids: Electrons in Periodic potential, Kronig-Penney Model, Bloch theorem and properties of Bloch wave, General symmetry properties, Nearly free electron model of metals, Extended, reduced and periodic zone scheme. Construction of Brillouin Zones in one and two dimensions, Classification of solids. Band structures, Metal, Insulator Semiconductor, Concepts of Effective mass, light and heavy holes in semiconductor.

Optical processes: Optical reflectivity of metal, Plasma frequency, Direct and indirect band gap of semiconductor, optical properties of semiconductors: Acceptor and donor level, Excitons and optical transitions in semiconductors, Absorption processes.

Dielectrics: Macroscopic description, electric polarisation and linear dielectrics, polarizability, sources of microscopic polarizations, theory of electronic, ionic and dipolar polarizability, local field and Clausius-Mossotti relation. Dipolar dispersion and Debye equation. Piezo-Pyro and Ferroelectric properties of crystals (qualitative discussion).

Magnetism: Origin of magnetic moments in atoms/ions, Hund’s rule, Crystal field effect, Quantum theory of paramagnetism and diamagnetism. Pauli paramagnetism Ferromagnetism: Exchange Interactions and magnetic-order, Weiss model of ferromagnetism, Magnetic domains. Band ferromagnetism & stoner criterion (qualitative discussion).

Superconductivity: Discovery, Critical temperature and Field, Perfect diamagnetism and Meissner effect, Type I and Type 2 superconductors, Phenomenological theory, London equations, thermodynamics: specific heat and energy gap, The isotope effects, Microscopic BCS theory (qualitative), Coherence of superconducting state, Flux quantization and Josephson effect (qualitative).

This module is intended to introduce various aspects of modern physics. The module includes the study of Atomic physics, Molecular structure and molecular spectra, Vibrations of diatomic molecules, Electronic structure and electronic spectra, Laser physics. Unit IV caters to national and global needs. 

Brief review of early atomic models of Bohr and Sommerfield. One electron atom - atomic orbitals, spectrum of hydrogen, Rydberg atoms, spin-orbit interaction and fine structure in alkali spectra. Equivalent and non-equivalent electrons. Zeeman Effect, Paschen Back Effect, Stark Effect, Lamb shift in hydrogen (qualitative). Two electron atom - ortho and para states, and role of Pauli Exclusion Principle, level schemes of two electron atoms. Many electron atoms - Central field approximation, LS and JJ coupling, multiplet splitting and Lande interval rule.

Diatomic molecules as a rigid rotor, rotational spectra of rigid and non-rigid rotors, intensity of rotational lines, types of rotor-linear, symmetric top, asymmetric top and spherical top molecules.

Diatomic molecules as simple harmonic oscillator, anharmonicity, Morse potential curve, vibrating rotator and spectra. Electronic spectra of diatomic molecules, vibrational coarse structure: progressions, intensity of vibrational-electronic spectra: Franck Condon principle, dissociation energy, rotational fine structure of electronic-vibrational transitions, Fortrat diagram, predissociation.

Laser: Coherence of light, coherence of time, coherence length, types of coherence: temporal and spatial, population inversion techniques: electrical and optical pumping, building up of laser action, criteria for lasing, threshold conditions, He-Ne laser: energy level diagram, principle, construction and working. Applications.

Optical fibres: Importance of fibre optics, fibre materials, types of optical fibres: single mode and multimode with different refractive index profiles (qualitatively). Ray theory transmission - total internal reflection, acceptance angle, numerical aperture, transmission characteristics of optical fibres - attenuation and dispersion, optical fibre communication system (qualitative).

[2].      Bransden B. H. and Joachain B. H. (1983). Physics of Atoms and Molecules: Longman Group Ltd.

The course aims to develop an understanding of fundamental aspects of material science. The course discusses the structure and imperfections of materials and its correlation with its properties. It also introduces students to a variety of functional materials, including metal alloys, ceramics, polymers and their applications. Unit IV caters to regional, national and global needs.

• Develop skills to understand various material properties, tackle research problems, and generate novel ideas on material science.
• Apply the fundamental knowledge gained on materials to cater to the needs of national and local needs. 

This course has been conceptualized in order to give students to get exposure to the fundamentals of Electronic Instrumentation. Students will be introduced to new ideas such as various types of sensors and transducers, and detectors used in data acquisition. They learn the basics of amplifiers and data acquisition, filters and general electronic instruments. Computer interface instrumentation and Arduino-based instrumentation are also covered in this topic.

This course provides the students with

1. Knowledge about different types of sensors and transducers,
2. Understanding the concept of data acquisitions, signal conditioning and PC based instrumentation.
3. Gaining basic skills needed for instrumentation and control
4. Relevant expertise in different control systems
5. Knowledge of PC based instrumentation to cater the needs of skill development and entrepreneurship

Transducers: Review on basic characteristics of measuring devices. Electrical transducer, Characteristics of a transducer. Variable inductance, capacitance and resistance transducer, Digital transducers. Wheatstone's strain gauge circuit. Piezoelectric pressure transducer, Resistance temperature sensors, Thermistor.

Detectors: Photo-electric effect, Photon Detectors: Classification – Photomultiplier – Photoconductive cell. Performance criterion - Noise consideration – Figure of merit. Characteristics parameter: sensitivity, noise, quantum efficiency, spectral response, Johnson noise, signal to noise ratio, background, calibration, Correlation measurements.

 Amplifiers & filters: Preamplifier, Instrumentation amplifiers, Isolation amplifiers, Review of filters - Passive and active filters - Butterworth Filters, First order filter & Second order filter-Low pass filter, High pass filter, Band pass filter, band reject filter and narrow band reject filter, All pass filter, Pass reject filter, Frequency to voltage and voltage to frequency converters.

Data Acquisition systems: Characteristics, Signal conditioning, Single channel acquisition system, Multichannel acquisition system, Multiplexer, Digital to analog converter –weighted resistor and R-2R network, Analog to digital converter – Sample and hold circuits, Successive approximation and dual slope.

Mathematical modelling - open-loop and closed-loop systems, the feedback concept, continuous-time systems modelling, Review of Laplace transform, transfer function, block diagrams, signal flow graph.

Analysis - time-domain solution of first-order systems, time constant, time-domain solution of second-order systems, determination of response for standard inputs using transfer functions, steady-state error, concept of stability, Routh Hurwitz techniques, construction of bode diagrams, phase margin, gain margin

General form of PC based instrumentation system, Functional blocks of data acquisition configurations. Data acquisition with serial interfaces, serial connection formats, serial communication modes, Features of USB, USB system, USB transfer, USB descriptors. Arduino basics – programming, interfacing modules-–Sensors, LCD, DC motor, camera. Signal acquisition using Arduino.

 [1].      Simon, M. (2016). Programming arduino: Getting started with sketches. New York, NY: Tata McGraw Hill.

 [1].      Nakra, B. C., & Chaudhary, K. K. (2004). Instrumentation measurement analysis. New York, NY: Tata McGraw Hill.

[3].      Patranibis, D. (1994). Principles of industrial instrumentation. New York, NY: Tata McGraw Hill.

Course description: This course will provide a basic introduction to various topics in astronomy such as Celestial sphere, an overview about various observing techniques in imaging and spectroscopy, a concise introduction to our Sun and provides a detailed outlook about various layers in the star and about the major heat transfer mechanisms. This course is even suited for a physics student who is not having a previous background in Astrophysics. Units II to IV caters to national and global needs. 

Course Objectives: On completion of this course the student will be able to: 

● Understand the evolutionary phase of a star from the knowledge of the magnitudes of the star in various passbands. 

● Explain how astronomical observations are performed and the relevance of multi-wavelength data to decode the nature of stellar systems. 

● Learn the energy generation processes in the stars and how that is used to understand the life cycle of the Sun. 

● Evaluate the aspects of the solar cycle and how space weather is modified due to the mass ejection mechanisms from the Sun in the form of Solar flares. 

Spectral classification of stars, Luminosity classification, Hertzsprung Russell diagram: magnitude, flux, luminosity, bolometric magnitude, bolometric correction; Distance modulus, Colour index, reddening, extinction; Colour temperature, Effective temperature; zero-age main sequence 

Stellar groups: Binaries, moving groups, star clusters. Stellar dynamics: Distance measurement methods, parallax, Proper motion, Radial Velocity, Glimpse of Gaia mission and related survey programs 

 Spherical Astronomy: Celestial sphere, Coordinate systems, Solar and Sidereal times, Observation techniques/methods: photometry, astrometry, spectroscopy, polarimetry, interferometry (qualitative discussion), Atmospheric transparency, Telescopes and detectors at different wavelengths, bandpass filters in optical and IR, active/adaptive optics. 

Spectroscopy: Brief overview of atomic and molecular spectra, Absorption and emission lines, signal to noise ratio; Boltzmann equation, Saha ionization formula, Excitation temperature, Kinetic temperature, Line broadening mechanisms, curve of growth analysis, Basic spectrograph design.

 Solar atmosphere: Interior of the Sun, Chromosphere, Corona, chromospheric heating, types of corona, correlation with optical depth, solar neutrino problem; Magnetic field in the Sun: sunspots, solar cycle, Butterfly diagram, Magnetic dynamo theory, solar wind, heliosphere, Sun-Earth interaction, Sun as a star, helioseismology, Active stars

Discussion on the planetary architecture of the solar system, Brief overview of the planetary atmospheres, formation of the solar system, Exoplanets: detection methods, Kepler mission results, planet migration, measuring the mass, radius and temperature of exoplanets, theories of planet formation.

Structure of low mass and high mass stars (qualitative), Hydrostatic equilibrium,  equation of state, mean molecular weight, expressions for gas pressure and radiation pressure, Gravitational potential energy, Kelvin-Helmholtz timescale, Nuclear fusion: Fusion reactions – p-p chain, CNO cycle, triple-alpha process, energy generation rate, nuclear timescale,  energy transport mechanisms in stars, temperature gradient for radiative and convective process, Overview of stellar structure equations, Schwarzschild criterion, Vogt-Russell theorem, mass - luminosity relation.

1. Foukal, P. V. (1990). Solar astrophysics: John Wiley.

2. Zirin, H. (1988). Astrophysics of the Sun: Cambridge University Press. 

3. Harwit, M. (1988). Astronomy concepts: Springer-Verlag.

4. Cox, J. P., & Giuli, R. T. (1968). Principles of stellar structure: Science Publishers, Gorden-Breach.

     CIA I - 20 marks (Research Based Assessment, Submission type assignment).

      CIA II - 20 marks (Descriptive type test and/or problem solving, Submission type).

      CIA III - 20 marks (Experiential learning, Submission type).

      ESE - 50 marks (Descriptive/Problem solving, Written type, finally converted to 40 marks).

The course will provide knowledge to the students on the fundamentals of solar radiation, solar cells, PV module system, and solar thermal collectors. This will enable learners to understand the requirements of PV and solar thermal systems for different household and commercial applications. 

Solar Radiation: The Sun and the Earth (Extra-terrestrial Solar Radiation, Solar Spectrum at the Earth's Surface), The Sun-Earth Movement (Declination Angle δ, Apparent Motion of the Sun and Solar Altitude), Air-Mass, Solar Day-length, Estimation of solar energy daily and monthly, Angle of Sunrays on Solar Collector, Sun Tracking, Estimating Solar Radiation Empirically, Measurement of Solar Radiation                               

P-N Junction Diode: An Introduction to Solar Cells: Why P-N Junction Diode?, Introduction to P-N Junction: Equilibrium Condition (Space Charge Region, Energy Band Diagram Of P-N Junction, P-N Junction Potential, Width of Depletion Region, Carrier Movement and Current Densities, Carrier Concentration Profile), P-N Junction in Non-Equilibrium Condition (P-N Junction I-V Relation: A Qualitative Analysis, P-N Junction I-V Relation: A Quantitative Analysis), P-N Junction Under Illumination: Solar Cell (Generation of Photovoltage, Light Generated Current, I-V Equation of Solar Cells, Solar Cell Characteristic).            

Design of Solar Cells: Upper Limits of Cell Parameters (Short Circuit Current, Open Circuit Voltage, Fill Factor, Efficiency), Losses in Solar Cells (Effect of Series and Shunt Resistance on Efficiency, Effect of Solar Radiation on Efficiency, Effect on Temperature on Efficiency, Ohmic losses, Optical losses, Shockley-Queisser limit), Solar Cell Design, Deigns for High Isc, Design for High Voc, Design for High FF, Analytical Techniques (Solar Simulator: I-V Measurement, Quantum Efficiency (QE) Measurement, Minority Carrier Lifetime and Diffusion Length Measurement)                                            

Si Wafer-Based Solar Cell Technology (1^st Generation): Process flow of Commercial Si Cell Technology, Processes used in Solar Cell Technologies (Saw Damage Removal and Surface Texturing, P-N Junction Formation: The Diffusion Process, Thin-film Layers for ARC and Surface Passivation, Metal Contacts: Pattern Defining and Deposition), High Efficiency Si Solar Cells (Passivated Emitter Solar Cells (PESC), Buried Contact Solar Cells, Rear Point Contact Solar Cells, Passivated Emitter and Rear Contact).

Thin Film Solar Cell Technologies (2^nd Generation):  Common features of thin film solar cell, Amorphous Si Solar Cell Technology, Cadmium Telluride Solar Cell Technology, Chalcopyrite (CIGS) Solar Cell Technology.

Concentrator PV Cells and Systems: Light Concentration, Concentration ratio, Optics for Concentrator PV (CPV) (V-trough Concentrator Modules, Compound Parabolic Concentrator (CPC) and Parabolic Trough Concentrator, Paraboloid Reflector Fresnel's Lens Concentrator), Tracking system, High Concentrator Solar Cells. 

Emerging Solar Cell Technologies And Concepts (3^rd Generation): Organic Solar Cells, Dye-sensitized Solar Cells (DSSC), GaAs Solar Cells, Perovskites solar cell, Quantum dot solar cells, Thermo-Photovoltaics (TPV), Beyond Single Junction Efficiency Limit, Approaches to Overcome Single Junction Efficiency Limit (Crystalline Si Multijunction Solar Cells I, Intermediate Band Gap, Impurity PV and Quantum Well Solar Cells, Spectrum Modification Approaches: Up and Down, Photon Energy Conversion, Hot Carrier Solar Cells)

Merits and demerits for all generations.

Solar Photovoltaic Modules: Solar PV Modules from Solar Cells (Series and Parallel Connection of Cells, Mismatch in Cell/Module), Mismatch in Series Connection, Mismatching in Parallel Connection, Design and Structure of PV Modules (Number of Solar Cells in a Module, Wattage of Modules, Fabrication of PV modules), PV Module Power Output (Ratings of PV Modules, Power Curve of Module, Effect of Solar Irradiation and Temperature)

Balance of Solar PV Systems: Basics of Electrochemical Cell (battery), Factors Affecting Battery Performance, batteries for PV Systems, DC to DC Converters, Charge Controllers, DC to AC Converter, Maximum Power Point Tracking (MPPT)

Photovoltaic System Design And Applications: Introduction to Solar PV Systems, Standalone PV System Configurations (Type-a: Standalone System with DC Load, Type-b: Standalone System with DC Load, Type-c: Standalone System with Battery and DC Load, Type-d: Standalone System with Battery and AC/DC Load, Type-e: Hybrid System with AC/DC Load, Type-f: Grid-connected System without Energy Storage), Design Methodology of PV Systems, Standalone System with DC Load using MPPT (Type-b Configuration), Design of PV Powered DC Pump, Design of Standalone System with Battery and AC/DC Load, Wire Sizing in PV Systems, Precise Sizing of PV Systems, Hybrid PV Systems, Grid-connected PV Systems, Simple Payback Period, Lifecycle Costing (LCC), Case studies on designing PV systems, PV solar Grid Architecture, Implications of latitude, shading, temperature, and system geometry.  

[2].         Tiwari G.N., (2009) Solar Energy: Fundamentals, Design, Modelling and Applications, Narosa Publishing House.

[3].         Khan B.H., (2006) Non-conventional energy resources. New Delhi: TMH publishing.

[2].         Solanki C.S (2015) Solar Photovoltaics - Fundamentals, Technologies and Applications, PHI Learning; 3rd edition.

[3].         Roger A.M. and Ventre J.,(2000) Photovoltaic systems engineering, CRC Press.

[4].         Arno Smets, Klaus Jäger, Olindo Isabella, René van Swaaij, Miro Zeman, (2016) Solar Energy: The Physics and Engineering of Photovoltaic Conversion, Technologies and Systems, UIT Cambridge.

[5].         Avram Mse, Lacho Pop Mse, (2015) The Ultimate Solar Power Design Guide: Less Theory More Practice, DIMI Digital Publishing Ltd,.

The experiments related to atomic, molecular, nuclear and solid-state physics included in this course expose the students to many fundamental experiments in physics and their detailed analysis and conclusions. This provides a strong foundation to the understanding of physics.

1. Study of nuclear counting statistics.
2. Study of absorption of β particles in Al, range and end-point energy of β particles in Al.
3. Study of g-ray spectrum of Cs-137 using gamma ray spectrometer (using SCA & MCA)
4. Study of attenuation of γ rays in lead using NaI(Tl) detector spectrometer.
5. Study of Hall effect in semiconductors.
6. Determination of Lande’s g-factor using ESR spectrometer.
7. Study of emission spectrum of neon using constant deviation spectrograph.
8. Study of vibrational band spectrum of aluminum oxide.
9. Determination of magnetic susceptibility by Quinke’s method.
10. Study of Zeeman effect- Determination of e/m for an electron.
11. Analysis of NMR spectrum of 2-3 dibromopropionic acid. 
12. Analysis of IR spectrum of Benzaldehyde.

Virtual / simulation based experiments

1. Study of nuclear counting statistics.
2. Energy calibration of gamma ray spectrometer and the study of gamma- ray spectrum of Cs-137.
3. Study of mass attenuation coefficient of X-rays and γ ray.
4. Study of Hall effect in semiconductors

This practical lab course provides hands-on practice on optical, thermal, electrical and magnetic characterizations of materials. 

• Develop practical-skills to tackle research problems and design novel materials and devices.
• Apply the practical knowledge gained about material property measurements to develop functional materials for various applications to cater the national and local energy needs.
• Seek employability in the area of material science-based industries.

1. Determination of piezoelectric constant of PTFE.
2.  Measurement Of susceptibility of solids by Gouy's Method.
3. Study of variation of dielectric constant with temperature-ferroelectric sample.
4.  Study of thermal expansion of a crystal by optical interference method
5. Measurement of ionic conductivity of crystals
6. Deposition of metallic thin films using thermal evaporation setup and determination of resistivity
7. Energy band gap of Ge using Four Probe method
8. Determination of the band gap of the semiconductor and change in concentration of organic compound from the UV-Vis absorbance curve
9. Synthesis of nano-catalyst by chemical method and study its catalytic behaviour for H2 production
10. Synthesis of KCl crystals and determination of density by floatation method.
11. Triple point of water.

Virtual / simulation based experiments

1. Tensile Test on Mild Steel

2. Resistivity of a Semiconductor by Four Probe Method

3. Compression Test on Mild Steel

This lab module makes the students familiar with the design and working electronic instruments employed for the measurement of various physical parameters in a laboratory environment.

1. Analog to digital conversion (ADC) using AD ADC 0804
2. Digital to analog converter (DAC) -by IC MC1408 and current to voltage converter.
3. Instrumentation amplifier –Using OP-AMP and transducer bridge
4. Adjustable voltage and current regulator using LM317
5. Dual voltage regulator using 78XX and 79XX and bridge rectifier
6. Experiments with phase sensitive detector - Mutual inductance of a coil and low resistance of copper
7. Arduino - Interfacing LED and LCD
8. Arduino - Interfacing Sensors - Distance measurement using ultrasonic sensor.
9. Arduino - Interfacing Temperature sensor – Simulations
10. Arduino - Interfacing camera module and image acquisition.
11. Creating Transfer functions in GNU Octave
12. Time domain analysis using GNU Octave
13. Block diagram reduction using GNU Octave

[2].      Mathivanan, N. (2007). PC based instrumentation. New Delhi: Prentice-Hall of India.

[3].      Nagarath I. J. & Gopal M., (2018) Control System Engineering, 6th Edition, New Age International Pvt. Ltd.,

[2].      Nakra, B. C., & Chaudhary, K. K. (2004). Instrumentation measurement analysis. New York, NY: Tata McGraw Hill.

[3].      Kalsi, H. S. (1997). Electronic instrumentation. New York, NY: Tata McGraw Hill.

These laboratory experiments are designed to expose the students to contemporary research in observational astronomy. The experiments in this semester are particularly focused on astronomical spectroscopy. Since the description about spectroscopy and imaging is provided in the theory class, the experiments follow the regular course.

1. Study of spectral energy distribution (SED) of stars

2. Discussion on IR excess from the SED of young stars.

3. Estimation of the period of rotation of the Sun using CLEA.

4. Construction of the HR diagram of stars in the solar neighbourhood.

5. Determination of the age of selected star clusters

6. Estimate the cluster distance from main sequence fitting using Padova/MESA models.

7. To study the proper motion of stars in clusters and moving groups.

8. Membership analysis of stars in a cluster using data from Gaia mission.

Additional experiments

● Aperture photometry using IRAF

● PSF photometry to estimate the magnitudes of stars in clusters

● Optical and infrared photometric observations of stars taken using the Indian telescopes such as HCT and VBT.

This practical lab course is planned to provide the hands-on practice to design and measure the operational parameters of solar cells, solar collectors, and solar PV systems. Students will be given proper exposure to the software for investigating the performance of the designed solar energy devices. Aerodynamics of wind turbines and energy potential of biomass will be investigated experimentally.

1.Determine the performance parameters of solar-cell using IV curve and verify inverse square law. 

2.Study the characteristic of single-crystal and multi-crystalline Si solar cells. 

3.Design PN junction Si solar cell with efficiency above 15 % and fill factor above 75 % using the SCAPS software. 

4.Study the effect of intensity of solar radiation, different angle, wavelength and temperature on the performance of the solar-cell.

5.Study the efficiency of solar cells connected in series, or/and parallel.

6.Fabricate Dye-sensitized solar cell in Lab using TiO2 on ITO/FTO glass. 

7.Design multijunction solar-cell using SCAPS software with efficiency above 25 %. 

8.Design the solar farm using PV-SYST software to fulfil the large scale power requirement.

9.Evaluate the performance parameters (Efficiency, heat loss and removal factors) of the solar water heater setup.  

10. Heat transfer analysis of a receiver tube of parabolic trough solar collector using ANSYS software.

[2].Khan B.H., (2006) Non-conventional energy resources. New Delhi: TMH publishing.

[3].Sathyajith Mathew, (2006) Wind Energy: Fundamentals, Resource Analysis and Economics, Springer.

[5].Tiwari G.N., (2009) Solar Energy: Fundamentals, Design, Modelling and Applications, Narosa Publishing House. 

[6].Roger A.M. and Ventre J.,(2000) Photovoltaic systems engineering, CRC Press. 

[7].Arno Smets, Klaus Jäger, Olindo Isabella, René van Swaaij, Miro Zeman, (2016) Solar Energy: The Physics and Engineering of Photovoltaic Conversion, Technologies and Systems, UIT Cambridge.

[8].Siraj Ahmed, (2016) Wind Energy: Theory and Practice,  PHI Learning; 3rd edition.

[9].John Andrews and Nick Jelley (2013) Energy Science: Principles, Technologies, and Impacts, Oxford publication. 

[10].Efstathios E. (Stathis) Michaelides, (2012) Alternative Energy Sources, Springer.

[11].Donald L. Klass, (1998) Biomass for Renewable Energy, Fuels and Chemicals, Elsevier.

Assessment scheme for end semester practical examination 

Principle, procedure, circuit  : 10 

Experimental setup, wiring            : 10 

Taking readings                            : 10 

Graphs, calculations and results     : 10 

Viva related to the experiment       : 10 

Total marks                                  : 50 

In the framework of the Master's dissertation course, the students will explore various aspects of initiating and executing a research project. This course includes the stages of defining a topic and formulating a problem statement, selecting and reviewing relevant literature, designing an empirical study as well as performing it, including data collection and analysis, make theoretical conclusions, and finally writing a report called Master's dissertation.

Dissertation will be group work, guided by faculty. The student is expected to carry out a literature survey and select unresolved problems in the domain of the selected research topic. They also gain the expertise to use tools and techniques for the objectives of the study. This paper addresses the cross-cutting issues such as ethics in research and social responsibility.