SPS offers Masters in three streams, namely, Physics, Chemistry and Mathematics. The details of the courses under these programmes are available through the following respective links: I. Courses for M.Sc. in Physics II. Courses for M.Sc. in Chemistry III. Courses for M.Sc. in Mathematics 
I. Courses for M.S.c. in Physics
Semester I

Semester II

Electronics PS 425 (2 credits)  Mathematical Physics II PS 428 (2 credits) 
Physics Lab I PS 415 (6 credits)




Semester III

Semester IV

Condensed Matter Physics PS 511 (3 credits) 
Elective II (3 credits) 
Subatomic Physics PS 512 (3 credits)  Elective III (3 credits) 
Atoms and Molecules PS 514 (3 credits)  Project (4 credits) PS 522 
Physics Lab III PS 515 (6 credits) 
SEMESTER I
 Mathematical Physics I (3 credits) PS 417
 Classical Mechanics (3 credits) PS 412
 Quantum Mechanics I (3 credits) PS 413
 Electronics (2 credits) PS 425
 Physics Lab I (6 credits) PS 415
Total 17 credits
PS 417 Mathematical Physics I (3 credits)
Linear Vector Spaces
Linear vector spaces, dual space, inner product spaces. Linear operators, matrices for linear operators. Eigenvalues and eigenvectors. Similarity transformation, (matrix) diagonalization. Special matrices: Normal, Hermitian and Unitary matrices. Hilbert space.
Complex Analysis
Complex numbers and variables. Complex analyticity, CauchyRiemann conditions. Classification of singularities. Cauchy's theorem. Residues. Evaluation of definite integrals. Taylor and Laurent expansions. Analytic continuation, Gamma function, zeta function. Method of steepest descent.
Ordinary Differential Equations and Special Functions
Linear ordinary differential equations and their singularities. Sturm Liouville problem, expansion in orthogonal functions. Series solution of secondorder equations. Hypergeometric function and Bessel functions, classical polynomials. Fourier Series and Fourier Transform.
References:
 G.B. Arfken, Mathematical Methods for Physicists, Elsevier
 P. Dennery and A. Krzywicki, Mathematics for Physicists, Dover
 S.D. Joglekar, Mathematical Physics: Basics (Vol. I) and Advanced (Vol. II), Universities Press
 A.W. Joshi, Matrices and Tensors in Physics, New Age Publishers
 R.V. Churchill and J.W. Brown, Complex Variables and Applications, McGrawHill
 P.M. Morse and H. Feshbach, Methods of Theoretical Physics (Vol. I & II), Feshbach Publishing
 M.R. Spiegel, Complex Variables, McGrawHill
PS 412 Classical Mechanics (3 credits)
Lagrangian and Hamiltonian Formulations of Mechanics
Calculus of variations, Hamilton's principle of least action, Lagrange's equations of motion. Symmetries and conservation laws, Noether’s theorem. Hamilton's equations of motion. Phase plots, fixed points and their stabilities.
TwoBody Central Force Problem
Equation of motion and first integrals. Kepler problem. Classification of orbits. Satellites and interplanetary orbits. Scattering in central force field.
Small Oscillations
Linearization of equations of motion. Normal coordinates. Damped and forced oscillations. Anharmonic terms, perturbation theory.
Rigid body dynamics
Rotational motion, moments of inertia, torque. Euler’s theorem, Euler angles. Symmetric top. Gyroscopes and their applications.
Hamiltonian Mechanics
Canonical transformations. Poisson brackets. HamiltonJacobi theory, actionangle variables. Integrable system. Perturbation theory. Introduction to chaotic dynamics.
References:
 H. Goldstein, C.P. Poole and J.F. Safko, Classical Mechanics, AddisonWesley
 N.C. Rana and P.S. Joag, Classical Mechanics, Tata McGrawHill
 J.V. Jose and E.J. Saletan, Classical Dynamics: A Contemporary Approach, Cambridge University Press
 L.D. Landau and E.M. Lifshitz, Mechanics, ButterworthHeinemann
 I.C. Percival and D. Richards, Introduction to Dynamics, Cambridge University Press
 R.D. Gregory, Classical Mechanics, Cambridge University Press
PS 413 Quantum Mechanics I (3 credits)
Introduction
Review of empirical basis, waveparticle duality, electron diffraction. Notion of state vector. Probability interpretation. Review and relations between approaches of HeisenbergBornJordan, Schroedinger and Dirac.
Structure of Quantum Mechanics
Operators and observables, operators as matrices, significance of eigenvalues and eigenfunctions. Commutation relations. Uncertainty principle. Measurement in quantum theory.
Quantum Dynamics
Timedependent Schrödinger equation. Stationary states and their significance. Timeindependent Schrödinger equation.
Schrödinger Equation for onedimensional systems
Freeparticle, periodic boundary condition. Wave packets. Square well potential. Numerical solution of Schroedinger equation. Transmission through a potential barrier. Gamow theory of alphadecay. Field induced ionization, Schottky barrier. Simple harmonic oscillator: solution by wave equation and operator method. Charged particle in a uniform magnetic field. Coherent states.
Spherically Symmetric Potentials
Separation of variables in spherical polar coordinates. Orbital angular momentum, parity. Spherical harmonics. Free particle in spherical polar coordinates. Spherical well. Hydrogen atom. Numerical solution of the radial equation in arbitrary potential.
References:
 C. CohenTannoudji, B. Diu and F. Laloe, Quantum Mechanics (Vol. I), Wiley
 L.I. Schiff, Quantum Mechanics, McGrawHill
 R. Shankar, Principles of Quantum Mechanics, Springer
 E. Merzbacher, Quantum Mechanics, John Wiley and Sons
 A. Messiah, Quantum Mechanics (Vol. I), Dover
 A. Das, Lectures on Quantum Mechanics, Hindustan Book Agency
 R.P. Feynman, Feynman Lectures on Physics (Vol. III), AddisonWesley
 A. Levi, Applied Quantum Mechanics, Cambridge Univ Press
PS 425 Electronics (2 credits)
Introduction
Survey of network theorems and network analysis, AC and DC bridges, transistors at low and high frequencies, FET.
Electronic Devices
General properties of semiconductors. Schottky diode, pn junction, Diodes, lightemitting diodes, photodiodes, negativeresistance devices, pnpn characteristics, transistors (FET, MoSFET, bipolar).
Basic differential amplifier circuit, operational amplifier  characteristics and applications, simple analog computer, analog integrated circuits.
Digital Electronics
Gates, combinational and sequential digital systems, flipflops, counters, multichannel analyzer.
References:
 P. Horowitz and W. Hill, The Art of Electronics, Cambridge University Press
 J. Millman and A. Grabel, Microelectronics, McGrawHill
 J.J. Cathey, Schaum's Outline of Electronic Devices and Circuits, McGrawHill
 M. Forrest, Electronic Sensor Circuits and Projects, Master Publishing Inc
 W. Kleitz, Digital Electronics: A Practical Approach, Prentice Hall
 J.H. Moore, C.C. Davis and M.A. Coplan, Building Scientific Apparatus, Cambridge University Press
PS 415 Physics Laboratory I (6 credits)
 Error analysis
 G.M Counter
 Experiments with microwaves
 Resistivity of semiconductors
 Work function of Tungsten
 Hall effect
 Thermal conductivity of Teflon
 Susceptibility of Gadolinium
 Transmission line, propagation of mechanical and EM waves
 Measurement of e/m using Thomson method
 Measurement of Planck’s constant using photoelectric effect
 Michelson interferometer
 Millikan oildrop experiment
 FrankHertz experiment
 Experiment using semiconductor laser
Note: Each student is required to perform at least 8 of the above experiments.
SEMESTER II
 Quantum Mechanics II (3 credits) PS 421
 Statistical Mechanics (3 credits) PS 429
 Electromagnetic Theory (3 credits) PS 423
 Mathematical Physics II (2 credits) PS 428
 Relativistic Physics (2 credits) PS 424
 Physics Laboratory II (Electronics) (4 credits)
PS 426
Total 17 credits
PS 421 Quantum Mechanics II (3 credits)
Symmetry in Quantum Mechanics
Symmetry operations and unitary transformations. Conservation laws. Space and time translations; rotation. Discrete symmetries: Space inversion, time reversal and charge conjugation. Symmetry and degeneracy.
Angular momentum
Rotation operator, generators of infinitesimal rotation, angular momentum algebra, eigenvalues of J^{2} and J_{z}. Pauli matrices and spinors. Addition of angular momenta.
Identical particles
Indistinguishability, symmetric and antisymmetric wave functions, incorporation of spin, Slater determinants, Pauli exclusion principle.
Timeindependent Approximation Methods
Nondegenerate and degenerate perturbation theory. Stark effect, Zeeman effect and other examples. Variational methods. WKB approximation. Tunnelling. Numerical perturbation theory, comparison with analytical results.
Timedependent Problems
Schrödinger and Heisenberg pictures. Timedependent perturbation theory. Transition probability calculations, Fermi’s golden rule. Adiabatic and sudden approximations. Beta decay. Interaction of radiation with matter. Einstein A and B coefficients, introduction to the quantization of electromagnetic field.
Scattering Theory
Differential scattering crosssection, scattering of a wave packet, integral equation for the scattering amplitude, Born approximation, method of partial waves, low energy scattering and bound states, resonance scattering.
References:
Same as in Quantum Mechanics I plus
 C. CohenTannoudji, B. Diu and F. Laloe, Quantum Mechanics (Vol. II), Wiley
 A. Messiah, Quantum Mechanics (Vol.II), Dover
 S. Flügge, Practical Quantum Mechanics, Springer
 J. J. Sakurai, Modern Quantum Mechanics, Pearson
 K. Gottfried and T.M. Yan, Quantum Mechanics: Fundamentals, Springer
PS 429 Statistical Mechanics (3 credits)
Elementary Probability Theory
Binomial, Poisson and Gaussian distributions. Central limit theorem.
Review of Thermodynamics
Extensive and intensive variables. Laws of thermodynamics. Legendre transformations and thermodynamic potentials. Maxwell relations. Applications of thermodynamics to (a) ideal gas, (b) magnetic material, and (c) dielectric material.
Formalism of Equilibrium Statistical Mechanics
Phase space, Liouville's theorem. Basic postulates of statistical mechanics. Microcanonical, canonical, grand canonical ensembles. Relation to thermodynamics. Fluctuations. Applications of various ensembles. Equation of state for a nonideal gas, Van der Waals' equation of state. Meyer cluster expansion, virial coefficients. Ising model, mean field theory.
Quantum Statistics
FermiDirac and BoseEinstein statistics.
Ideal Bose gas, Debye theory of specific heat, properties of blackbody radiation. BoseEinstein condensation, experiments on atomic BEC, BEC in a harmonic potential.
Ideal Fermi gas. Properties of simple metals. Pauli paramagnetism. Electronic specific heat. White dwarf stars.
References:
 F. Reif, Fundamentals of Statistical and Thermal Physics, Levant
 K. Huang, Statistical Mechanics, Wiley
 R.K. Pathria, Statistical Mechanics, Elsevier
 D.A. McQuarrie, Statistical Mechanics, University Science Books
 S.K. Ma, Statistical Mechanics, World Scientific
 R.P. Feynman, Statistical Mechanics, Levant
 D. Choudhury and D. Stauffer, Principles of Equilibrium Statistical Mechanics, WileyVCH
PS 423 Electromagnetic Theory (3 credits)
Review of Electrostatics and Magnetostatics (23 weeks)
Coulomb’s law, actionata distance vs. concept of fields, Poisson and Laplace equations, formal solution for potential with Green's functions, boundary value problems; multipole expansion; Dielectrics, polarization of a medium; BiotSavart law, differential equation for static magnetic field, vector potential, magnetic field from localized current distributions; Faraday's law of induction; energy densities of electric and magnetic fields.
Maxwell’s Equations
Maxwell’s equations in vacuum. Vector and Scalar potentials in electrodynamics, gauge invariance and gauge fixing, Coulomb and Lorenz gauges. Displacement current. Electromagnetic energy and momentum. Conservation laws. Inhomogeneous wave equation and its solutions using Green’s function method. Covariant formulation of Maxwell’s equations (brief discussion).
Electromagnetic Waves
Plane waves in a dielectric medium, reflection and refraction at dielectric interfaces. Frequency dispersion in dielectrics and metals. Dielectric constant and anomalous dispersion. Wave propagation in one dimension, group velocity. Metallic wave guides, boundary conditions at metallic surfaces, propagation modes in wave guides, resonant modes in cavities. Dielectric waveguides. Plasma oscillations.
Radiation
EM Field of a localized oscillating source. Fields and radiation in dipole and quadrupole approximations. Antenna; Radiation by moving charges, LienardWiechert potentials, total power radiated by an accelerated charge, Lorentz formula.
References:
 D.J. Griffiths, Introduction to Electrodynamics, Prentice Hall
 J.D. Jackson, Classical Electrodynamics, Wiley
 A. Das, Lectures on Electromagnetism, Hindustan Book Agency
 J.R. Reitz, F.J. Milford and R.W. Christy, Foundations of Electromagnetic Theory, AddisonWesley
 W.K.H. Panofsky and M. Phillips, Classical Electricity and Magnetism, Dover
 R.P. Feynman, Feynman Lectures on Physics (Vol. II), AddisonWesley
 A. Zangwill, Modern Electrodynamics, Cambridge Univ Press
PS 428 Mathematical Physics II (2 credits)
Calculus of variations
Extremization problems (with and without constraints). EulerLagrange equations and Lagrange’s multipliers. Functional derivatives for real and complex fields (with applications in classical and quantum physics). Noether’s theorem.
Partial Differential Equations
Laplace and Poisson equation (with particular emphasis on solving boundary value problems in Electrostatics and Magnetostatics); Wave equation. Heat Equation. Green’s function approach. Separation of variables and solution in different coordinates.
Group Theory
Definition and properties. Discrete and continuous groups. Subgroups and cosets. Products of groups.
Matrix representation of a group. (Ir)reducible reprsentations. Characters. Representations of finite groups.
Examples of continuous groups, SO(3), SU(2) and SO(n) and SU(n). Generators of SU(2) and their algebra. Representations of SU(2).
References:
 P. Dennery and A. Krzywicki, Mathematics for Physicists, Dover
 S.D. Joglekar, Mathematical Physics: Advanced Topics (Vol. II), Universities Press
 P.M. Morse and H. Feshbach, Methods of Theoretical Physics (Vol. I & II), Feshbach Publishing
 A.W. Joshi, Matrices and Tensors in Physics, New Age Publishers
 W.K. Tung, Group Theory in Physics, World Scientific
 A. Das and S. Okubo, Lie Groups and Lie Algebras for Physicists, Hindustan Book Agency
 I. Gelfand and S. Fomin, Calculus of Variations, Dover
 W. Yourgrau and S. Mandelstam, Variational Principles in Dynamics and Quantum Theory, Dover
PS 424 Relativistic Physics (2 credits)
Special Theory of Relativity
Motivation. Postulates of special theory of relativity. Lorentz transformation. Spacetime diagram. Time dilation and length contraction. Addition of velocities. Doppler effect. Paradoxes.
Fourvectors, contra and covariant vectors. Coordinate, velocity and momentum fourvectors.
Tensors. Electromagnetic field tensor. Maxwell's equations in tensor notation. Transformation of electromagnetic field. Relativistic dynamics of charged particles in electromagnetic field with special emphasis on particle accelerators. Relativistic Lagrangian of charged particles in electromagnetic fields.
Relativistic Quantum Mechanics
KleinGordon equation and its plane wave solution.
Dirac matrices. Dirac equation. Plane wave solutions, intrinsic spin and magnetic moment. Antiparticles.
Dirac equation for the hydrogen atom. Spinorbit coupling and fine structure.
References:
 H. Goldstein C.P. Poole and J.F. Safko, Classical Mechanics, AddisonWesley
 A.P. French, Special Relativity, W.W. Norton
 E.F. Taylor and J.A. Wheeler, Spacetime Physics: Introduction to Special Relativity, W.H. Freeman
 W. Rindler, Introduction to Special Relativity, Oxford University Press
 J.D. Jackson, Classical Electrodynamics, Wiley
 L. Schiff, Quantum Mechanics, McGrawHill
 B.H. Bransden and C.J. Joachain, Quantum Mechanics, Pearson
 D. Styer, Relativity for the Questioning Mind, Johns Hopkins Univ Press
PS 426 Physics Laboratory II (Electronics) (4 credits)
 Circuit analysis using Thevenin's theorem and Kirchhoff’s law.
 Characteristics of diode, BJT, FET, FETswitch
 Analysis of feedback circuits
 Differential amplifier and current mirror circuits
 Characteristics of OPAMP and Trigger circuit
 Digital electronics
SEMESTER III
 Computational Physics (3 credits) PS 427
 Condensed Matter Physics (3 credits) PS 511
 Subatomic Physics (3 credits) PS 512
 Atoms and Molecules (3 credits) PS 514
 Physics Lab III (6 credits) PS 515
Total 18 credits
PS 427 Computational Physics (3 credits)
Overview
Computer organization, hardware, software. Scientific programming in FORTRAN and/or C, C++. Introduction to Mathematica and/or Matlab
Numerical Techniques
Sorting, interpolation, extrapolation, regression, numerical integration, quadrature, random number generation, linear algebra and matrix manipulations, inversion, diagonalization, eigenvectors and eigenvalues, integration of initialvalue problems, Euler, RungeKutta, and Verlet schemes, root searching, optimization.
Simulation Techniques
Monte Carlo methods, molecular dynamics, simulation methods for the Ising model and atomic fluids, simulation methods for quantummechanical problems, timedependent Schrödinger equation. Langevin dynamics simulation.
References:
 V. Rajaraman, Computer Programming in Fortran 77, Prentice Hall
 W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press
 H.M. Antia, Numerical Methods for Scientists and Engineers, Hindustan Book Agency
 D.W. Heermann, Computer Simulation Methods in Theoretical Physics, Springer
 H. Gould and J. Tobochnik, An Introduction to Computer Simulation Methods, AddisonWesley
 J.M. Thijssen, Computational Physics, Cambridge University Press
PS 511 Condensed Matter Physics (3 credits)
Metals
Drude theory, DC conductivity, Hall effect and magnetoresistance, AC conductivity, thermal conductivity, thermoelectric effects, FermiDirac distribution, thermal properties of an electron gas, WiedemannFranz law, critique of freeelectron model.
Crystal Lattices
Bravais lattice, symmetry operations and classification of Bravais lattices, common crystal structures, reciprocal lattice, Brillouin zone, Xray diffraction, Bragg's law, Von Laue's formulation, diffraction from noncrystalline systems.
Classification of Solids
Band classifications, covalent, molecular and ionic crystals, nature of bonding, cohesive energies, hydrogen bonding.
Electron States in Crystals
Periodic potential and Bloch's theorem, weak potential approximation, energy gaps, Fermi surface and Brillouin zones, Harrison construction, level density. Motion of electrons in optical lattices.
Electron Dynamics
Wave packets of Bloch electrons, semiclassical equations of motion, motion in static electric and magnetic fields, theory of holes.
Lattice Dynamics
Failure of the static lattice model, harmonic approximation, vibrations of a onedimensional lattice, onedimensional lattice with basis, models of threedimensional lattices, quantization of vibrations, Einstein and Debye theories of specific heat, phonon density of states, neutron scattering.
Semiconductors
General properties and band structure, carrier statistics, impurities, intrinsic and extrinsic semiconductors, equilibrium fields and densities in junctions, drift and diffusion currents.
Magnetism
Diamagnetism, paramagnetism of insulators and metals, ferromagnetism, CurieWeiss law, introduction to other types of magnetic order.
Superconductors
Phenomenology, review of basic properties, thermodynamics of superconductors, London's equation and Meissner effect, TypeI and TypeII superconductors.
References:
 C. Kittel, Introduction to Solid State Physics, Wiley
 N.W. Ashcroft and N.D. Mermin, Solid State Physics, Brooks/Cole
 J.M. Ziman, Principles of the Theory of Solids, Cambridge University Press
 A.J. Dekker, Solid State Physics, Macmillan
 G. Burns, Solid State Physics, Academic Press
 M.P. Marder, Condensed Matter Physics, Wiley
PS 512 Subatomic Physics (3 credits)
Nuclear Physics
Discovery of the nucleus, Rutherford scattering. Scattering crosssection, form factors. Kinematics of (non)relativistic scattering. Properties of nuclei: size, mass, charge, angular momentum, magnetic moment, parity, quadrupole moment. Charge and mass distribution.
Mass defect, bindingenergy statistics, BetheWeiszacker mass formula. Magic numbers, shell model, parity and magnetic moment.
Nuclear stability: alpha, beta and gamma decay. Tunnelling theory of alpha decay, Fermi theory of beta decay. Parity violation. Fission and fusion. Nuclear reaction.
Nuclear force. Nuclear reaction. Deuteron, properties of nuclear potentials. Yukawa's hypothesis.
Particle Physics
Discovery of elementary particles in cosmic rays. Muon, meson and strange particles. Isospin and strangeness.
Accelerators and detectors.
Quark hypothesis, flavour and colour. Meson and Baryon octets. GellmannNishijima formula. Discovery of J/psi, charm quark. Families of leptons and quarks. Bottom and top quarks.
Gauge symmetry and fundamental forces. Weak interaction, W and Z bosons, Higgs mechanism and spontaneous symmetry breaking. Higgs particle. Gluons and strong interaction.
Neutrino oscillations, CP violation.
References:
 B.L. Cohen, Concepts of Nuclear Physics, Tata McGraw Hill
 W.N. Cottingham and D.A. Greenwood, An introduction to Nuclear Physics, Cambridge University Press
 I. Kaplan, Nuclear Physics, AddisonWesley
 B.R. Martin, Nuclear and Particle Physics, Wiley
 A. Das and T. Ferbel, Introduction to Nuclear and Particle Physics, World Scientific
 B. Povh, K. Rith, C. Scholtz and F. Zetsche, Particles and Nuclei, Springer
 G.D. Coughlan and J.E. Dodd, The Ideas of Particle Physics, Cambridge University Press
 D. Griffiths, Introduction to Elementary Particles, Wiley
 D.H. Perkins, Introduction to High Energy Physics, Cambridge University Press
PS 514 Atoms and Molecules (3 credits)
Manyelectron Atoms
Review of H and He atom, ground state and first excited state, quantum virial theorem. Determinantal wave function. ThomasFermi method, Hartree and HartreeFock method, density functional theory. Periodic table and atomic properties: ionization potential, electron affinity, Hund's rule.
Molecular Quantum Mechanics
Hydrogen molecular ion (numerical solution), hydrogen molecule, HeitlerLondon method, molecular orbital, BornOppenheimer approximation, bonding, directed valence. LCAO.
Atomic and Molecular Spectroscopy
Fine and hyperfine structure of atoms, electronic, vibrational and rotational spectra for diatomic molecules, role of symmetry, selection rules, term schemes, applications to electronic and vibrational problems. Raman spectroscopy.
Second Quantization
Basis sets for identicalparticle systems, number space representation, creation and annihilation operators, representation of dynamical operators and the Hamiltonian, simple applications.
Interaction of Atoms with Radiation
Atoms in an electromagnetic field, absorption and induced emission, spontaneous emission and linewidth, Einstein A and B coefficients, density matrix formalism, twolevel atoms in a radiation field.
References:
 B.H. Bransden and C.J. Joachain, Physics of Atoms and Molecules, Pearson
 I.N. Levine, Quantum Chemistry, Prentice Hall
 L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Pergamon Press
 M. Karplus and R.N. Porter, Atoms and Molecules: An Introduction for Students of Physical Chemistry, W.A. Benjamin
 P.W. Atkins and R.S. Friedman, Molecular Quantum Mechanics, Oxford University Press
 W.A. Harrison, Applied Quantum Mechanics, World Scientific
 C.J. Foot, Atomic Physics, Oxford Univ Press
 G. Woodgate, Elementary Atomic Structure, Oxford Univ Press
PS 515 Physics Laboratory III (6 credits)
 Electron spin resonance
 Faraday rotation and Kerr effect
 Study of interfacial tension and viscosity of liquid
 Reaction kinetics by spectrometer and conductivity
 Experiment with Raman spectrometer
 Propagation of ultrasonic waves in liquid and solid
 Experiment with solar cell
 Dielectric constant of ice and ferroelectric transition of BaTiO_{3}
 Zeeman effect
 Study of superconducting properties in highT_{c} superconductor
 Scanning tunnelling microscopy
 Experiment with liquid using UV spectroscopy
Note: Each student is required to perform at least 8 of the above experiments.
SEMESTER IV
 PS 522 Project (4 credits)
(There will be midterm evaluation of the project)
In addition to the Project, a student has to choose any three among the following electives, each of 3 credits. Courses actually offered in a given semester will depend on the interests of the students and on the availability of instructors.
 Advanced Statistical Mechanics (PS 520)
 Astrophysics, Gravitation & Cosmology (PS 523)
 Quantum Field Theory (PS 524)
 Biophysics (PS 525)
 Laser Physics (PS 526)
 Advanced Condensed Matter Physics (PS 527)
 Nonlinear Dynamics (PS 528)
 Theory of Soft Condensed Matter (PS 529)
 Modern Experiments of Physics (PS 530)
Total 13 credits
PS 520 Advanced Statistical Mechanics
(3 credits)
Phase Transitions and Critical Phenomena
Thermodynamics of phase transitions, metastable states, Van der Waals' equation of state, coexistence of phases, Landau theory, critical phenomena at secondorder phase transitions, spatial and temporal fluctuations, scaling hypothesis, critical exponents, universality classes.
Mean Field Theory
Ising model, meanfield theory, exact solution in one dimension, renormalization in one dimension.
Nonequilibrium Statistical Mechanics
Systems out of equilibrium, kinetic theory of a gas, approach to equilibrium and the Htheorem, Boltzmann equation and its application to transport problems, master equation and irreversibility, simple examples, ergodic theorem.
Brownian motion, Langevin equation, fluctuationdissipation theorem, Einstein relation, FokkerPlanck equation.
Correlation Functions
Time correlation functions, linear response theory, Kubo formula, Onsager relations.
Coarsegrained Models
Hydrodynamics, NavierStokes equation for fluids, simple solutions for fluid flow, conservation laws and diffusion.
References:
 K. Huang, Statistical Mechanics, Wiley
 R.K. Pathria, Statistical Mechanics, Elsevier
 E.M. Lifshitz and L.P. Pitaevskii, Physical Kinetics, Pergamon Press
 D.A. McQuarrie, Statistical Mechanics, University Science Books
 L.P. Kadanoff, Statistical Physics: Statistics, Dynamics and Renormalization, World Scientific
 P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press
PS 523 Astrophysics, Gravitation & Cosmology
(3 credits)
General Theory of Relativity
Brief review of special theory of relativity, geometry of Minkowski spacetime. Curvilinear coordinates, covariant differentiation and connection. Curved space and curved spacetime. Contravariant and covariant indices. Metric tensor. Christoffel connection. Geodesics. Riemann, Ricci and Scalar curvature.
Principle of equivalence. Einstein equations in vacuum. Spherically symmetric solution, Schwarzschild geometry. Timelike and lightlike trajectories. Perihelion precession, bending of light in a gravitational field. Apparent singularity of the horizon, EddingtonFinkelstein and KruskalSzekeres coordinates. Penrose diagram.
Energymomentum tensor and Einstein equations. Weak field approximation, gravitational waves.
Physics of the Universe
Large scale homogeneity and isotropy of the universe. Expanding universe and Hubble’s law. FRW metric and Friedmann’s equations. Equations of state for matter (nonrelativistic dust), radiation and cosmological constant. Behaviour of scale factor for radiation, matter and cosmological constant domination. Big bang cosmology. Thermal history of the universe. Cosmic microwave background radiation and its anisotropy. Inflationary paradigm.
Astrophysics
Measuring distance and the astronomical ladder. Stellar spectra and structure, HertzsprungRussell diagram. Einstein equations for the interior of a star. Stellar evolution, nucleosynthesis and formation of elements. Main sequence stars, white dwarves, neutron stars, supernovae, pulsars and quasars.
References:
 B. Schutz, A First Course in General Relativity, Cambridge Univ Press
 S. Carroll, Spacetime and Geometry, Pearson
 S. Weinberg, Gravitation and Cosmology, Wiley
 J.V. Narlikar, An Introduction to Relativity, Cambridge Univ Press
 J. Hartle, Gravity, Pearson
 J.V. Narlikar, An Introduction to Cosmology, Cambridge Univ Press
 D. Maoz, Astrophysics in a Nutshell, Princeton University Press
 A. Rai Choudhuri, Astrophysics for Physicists, Cambridge Univ Press
 T. Padmanabhan, An Invitation to Astrophysics, World Scientific
PS 524 Quantum Field Theory (3 credits)
Examples of classical fields, vibrating string and electromagnetic field. Canonical coordinates and momenta, Lagrangian and Hamiltonian formulation.
Relativistic scalar field and KleinGordon equation. Canonical quantization. Space of states, Fock space, vacuum states and excitations. Complex scalar field.
Noether theorem. Internal symmetries. Spacetime translations and energymomentum tensor. Elementary excitations and particles.
Lorentz and Poincare symmetry. Spinor and vector fields.
Correlators of free scalar field. Retarded, advanced Green functions, Feynman propagator. Coupling to external source and partition function. Time ordering and normal ordering. Wick’s theorem.
Dirac field. Lagrangian and Hamiltonian. Canonical quantization and anticommutators. Green’s function.
Interacting scalar field, phi4 and Yukawa interactions. Ising Model and scalar field theory. Interaction picture. Green’s functions of interacting field and perturbation theory. Feynman rules and Feynman diagrams.
LSZ reduction formula. Smatrix. Tree level correlators.
Loops and divergences. UV and IR divergences. Connected and disconnected diagrams. Examples of divergences in two and fourpoint correlators. Introduction to regularization and renormalization.
References:
 M. Maggiore, A Modern Introduction to Quantum Field Theory, Cambridge University Press
 P. Ramond, Field theory, a Modern Primer, AddisonWesley
 L. Ryder, Quantum Field Theory, Academic Press
 A. Altland and B. Simon, Condensed Matter Field Theory, Cambridge University Press
 M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory, Levant
 A. Zee, Quantum Field Theory in a Nutshell, Universities Press
PS 525 Biophysics (3 credits)
Introduction
Evolution of biosphere, aerobic and anaerobic concepts, models of evolution of living organisms.
Physics of Polymers
Nomenclature, definitions of molecular weights, polydispersity, degree of polymerization, possible geometrical shapes, chirality in biomolecules, structure of water and ice, hydrogen bond and hydrophobocity.
Static Properties
Random flight model, freelyrotating chain model, scaling relations, concept of various radii (i.e., radius of gyration, hydrodynamic radius, endtoend length), endtoend length distributions, concept of segments and Kuhn segment length, excluded volume interactions and chain swelling, Gaussian coil, concept of theta and good solvents with examples, importance of second virial coefficient.
Polyelectrolytes
Concepts and examples, DebyeHuckel theory, screening length in electrostatic interactions.
Transport Properties
Diffusion: Irreversible thermodynamics, GibbsDuhem equation, phenomenological forces and fluxes, osmotic pressure and second virial coefficient, generalized diffusion equation, StokesEinstein relation, diffusion in threecomponent systems, balance of thermodynamic and hydrodynamic forces, concentration dependence, Smoluchowski equation and reduction to FokkerPlanck equation, concept of impermeable and freedraining chains.
Viscosity and Sedimentation: Einstein relation, intrinsic viscosity of polymer chains, Huggins equation of viscosity, scaling relations, KirkwoodRiseman theory, irreversible thermodynamics and sedimentation, sedimentation equation, concentration dependence.
Physics of Proteins
Nomenclature and structure of amino acids, conformations of polypeptide chains, primary, secondary and higherorder structures, Ramachandran map, peptide bond and its consequences, pHpK balance, protein polymerization models, helixcoil transitions in thermodynamic and partition function approach, coilglobule transitions, protein folding, protein denaturation models, binding isotherms, binding equilibrium, Hill equation and Scatchard plot.
Physics of Enzymes
Chemical kinetics and catalysis, kinetics of simple enzymatic reactions, enzymesubstrate interactions, cooperative properties.
Physics of Nucleic Acids
Structure of nucleic acids, special features and properties, DNA and RNA, WatsonCrick picture and duplex stabilization model, thermodynamics of melting and kinetics of denaturation of duplex, loops and cyclization of DNA, ligand interactions, genetic code and protein biosynthesis, DNA replication.
Experimental Techniques
Measurement concepts and error analysis, light and neutron scattering, Xray diffraction, UV spectroscopy, CD and ORD, electrophoresis, viscometry and rheology, DSC and dielectric relaxation studies.
Recent Topics in BioNanophysics
References:
 H. Bohidar, Fundamentals of Polymer Physics and Molecular Biophysics, Cambridge Univ Press
 M.V. Volkenstein, General Biophysics, Academic Press
 C.R. Cantor and P.R. Schimmel, Biophysical Chemistry Part III: The Behavior of Biological Macromolecules, W.H. Freeman
 C. Tanford, Physical Chemistry of Macromolecules, John Wiley
 S.F. Sun, Physical Chemistry of Macromolecules: Basic Principles and Issues, Wiley
PS 526 Laser Physics (3 credits)
Introduction
Masers versus lasers, components of a laser system, amplification by population inversion, oscillation condition, types of lasers: solidstate (ruby, Nd:YAG, semiconductor), gas (HeNe, CO_{2}, excimer), liquid (organic dye) lasers.
AtomField Interactions
Lorenz theory, Einstein's rate equations, applications to laser transitions with pumping, two, three and fourlevel schemes, threshold pumping and inversion.
Optical Resonators
Closed versus open cavities, modes of a symmetric confocal optical resonator, stability, quality factor.
Semiclassical Laser Theory
Density matrix for a twolevel atom, Lamb equation for the classical field, threshold condition, disorderorder phase transition analogy.
Coherence
Concepts of coherence and correlation functions, coherent states of the electromagnetic field, minimum uncertainty states, unit degree of coherence, Poisson photon statistics.
Pulsed Operation of Lasers
Qswitching, electrooptic and acoustooptic modulation, saturable absorbers, modelocking.
Applications of Lasers
Introduction to atom optics, Doppler cooling of atoms, introduction to nonlinear optics: self(de) focusing, secondharmonic generation (phasematching conditions). Industrial and medical applications.
References:
 K. Thyagarajan and A.K. Ghatak, Lasers: Theory and Applications, Springer
 A.K. Ghatak and K. Thyagarajan, Optical Electronics, Cambridge University Press
 W. Demtroeder, Laser Spectroscopy, Springer
 B.B. Laud, Lasers and Nonlinear Optics, WileyBlackwell
 M. Sargent, M.O. Scully and W.E. Lamb, Jr., Laser Physics, Perseus Books
 M.O. Scully and M.S. Zubairy, Quantum Optics, Cambridge University Press
 P. Meystre and M. Sargent, Elements of Quantum Optics, Springer
 L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press
PS 527 Advanced Condensed Matter Physics
(3 credits)
Dielectric Properties of Solids
Dielectric constant of metal and insulator using phenomenological theory (Maxwell's equations), polarization and ferroelectrics, interband transitions, KramersKronig relations, polarons, excitons, optical properties of metals and insulators.
Transport Properties of Solids
Boltzmann transport equation, resistivity of metals and semiconductors, thermoelectric phenomena, Onsager coefficients. Quantum Hall Effect.
Manyelectron Systems
Sommerfeld expansion, HartreeFock approximation, exchange interactions. Density functional theory. Concept of quasiparticles, introduction to Fermi liquid theory. Screening, plasmons. Fractional quantum hall effect.
Introduction to Strongly Correlated Systems
Narrow band solids, Wannier orbitals and tightbinding method, Mott insulator, electronic and magnetic properties of oxides, introduction to Hubbard model.
Magnetism
Magnetic interactions, HeitlerLondon method, exchange and superexchange, magnetic moments and crystalfield effects, ferromagnetism, spinwave excitations and thermodynamics, antiferromagnetism.
Superconductivity
Basic phenomena, London equations, Cooper pairs, coherence, GinzburgLandau theory, BCS theory, Josephson effect, SQUID, excitations and energy gap, magnetic properties of typeI and typeII superconductors, flux lattice, introduction to hightemperature superconductors.
References:
 N.W. Ashcroft and N.D. Mermin, Solid State Physics, Brooks/Cole
 D. Pines, Elementary Excitations in Solids, AddisonWesley
 S. Raimes, The Wave Mechanics of Electrons in Metals, Elsevier
 P. Fazekas, Lecture Notes on Electron Correlation & Magnetism, World Scientific
 M. Tinkham, Introduction to Superconductivity, CBS
 M. Marder, Condensed Matter Physics, Wiley
 P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press
PS 528 Nonlinear Dynamics (3 credits)
Introduction to Dynamical Systems
Physics of nonlinear systems, dynamical equations and constants of motion, phase space, fixed points, stability analysis, bifurcations and their classification, Poincaré section and iterative maps.
Dissipative Systems
Onedimensional noninvertible maps, simple and strange attractors, iterative maps, perioddoubling and universality, intermittency, invariant measure, Lyapunov exponents, higherdimensional systems, Hénon map, Lorenz equations, fractal geometry, generalized dimensions, examples of fractals.
Hamiltonian Systems
Integrability, Liouville's theorem, actionangle variables, introduction to perturbation techniques, KAM theorem, areapreserving maps, concepts of chaos and stochasticity.
Advanced Topics
Selections from quantum chaos, cellular automata and coupled map lattices, pattern formation, solitons and completely integrable systems, turbulence.
References:
 E. Ott, Chaos in Dynamical Systems, Cambridge University Press
 E.A. Jackson, Perspectives of Nonlinear Dynamics (Vol. I and II), Cambridge University Press
 A.J. Lichtenberg and M.A. Lieberman, Regular and Stochastic Motion, Springer
 A.M. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization, Cambridge University Press
 M. Tabor, Chaos and Integrability in Nonlinear Dynamics, WileyBlackwell
 M. Lakshmanan and S. Rajasekar, Nonlinear Dynamics: Integrability, Chaos and Patterns, CRC Press
 H.J. Stockmann, Quantum Chaos: An Introduction, Cambridge University Press
 V. Arnold, Mathematical Methods of Classical Mechanics, Springer
PS 529 Theory of Soft Condensed Matter
(3 credits)
_{Review of statistical mechanics}
Partition function, free energy, entropy. Entropy and information. Ideal systems. Interacting systems: Ising model and phase transition. Approximate methods for interacting systems: mean field and generalizations.
Complex molecues
The cell, small molecules, proteins and nucleic acids. Stretching a single DNA molecule, the freely jointed chain, the onedimensional cooperative chain, the wormlike chain, zipper model, The helixcoil transition.
Biological matter
Polymer collapse: Flory's theory. Collapse of semiflexible polymers: lattice models and the tube model. The selfavoiding walk and the O(n) model. An introduction to protein folding and design. RNA folding and secondary structure. Protein and RNA mechanical unfolding. Molecular motors.
Physics of active matter
Active matter and selfpropelled dynamics. Dry active matter, model of flocking. Hydrodynamic equations of active gels, entropy production, conservation laws, Thermodynamics of polar systems. Fluxes, forces, and time reversal. Constitutive equations, Microscopic interpretation of the transport coefficients. Applications of hydrodynamic theory to phenomena in living cell: Derivation of Hydrodynamics from microscopic models of active matter, microscopic models of selfpropelled particles: motors and filaments.
Theoretical models of stochastic dynamics
Stochastic processes as an universal toolbox. Brownian Motion. Langevin Equation. FokkerPlanck description. Fluctuationdissipation relations. From stochastic dynamics to macroscopic equations Smoluchowski dynamics. From Smoluchowski to hydrodynamics.
Numerical methods
Complex fluids, soft matter, colloids. Lattice gas cellular automata models.
Lattice Boltzman equation.
References
1. K. Huang, Statistical Physics, Wiley
2. R.K. Pathria and P.D. Beale, Statistical Mechanics, Academic Press
3. K. Sneppen and G. Zocchi, Physics in Molecular Biology, Cambridge
4. P. Nelson, Biological Physics, Freeman
5. B. Alberts et al, Molecular Biology of the Cell, Garland
PS 530 Modern Experiments of Physics
(3 credits)
Note: This course will familiarize students with some landmark experiments in physics through the original papers which reported these experiments. A representative list is as follows:
 Mössbauer effect
 PoundRebka experiment to measure gravitational red shift
 Parity violation experiment of Wu et al
 Superfluidity of ^{3}He
 Cosmic microwave background radiation
 Helicity of the neutrino
 Quantum Hall effect  integral and fractional
 Laser cooling of atoms
 Ion traps
 BoseEinstein condensation
 Josephson tunneling
 Atomic clocks
 Interferometry for gravitational waves
 Quantum entanglement experiments: Teleportation experiment, Aspect's experiment on Bell's inequality
 Inelastic neutron scattering
 CP violation
 J/Psi resonance
 Verification of predictions of general theory of relativity by binarypulsar and other experiments
 Precision measurements of magnetic moment of electron
 Libchaber experiment on perioddoubling route to chaos
 Anfinson's experiment on protein folding
 Scanning tunnelling microscope
 Discovery of the Higgs particle
 Discovery of Neutrino oscillation
References
The original papers, review articles and Nobel Lectures constitute the resource material for this course.
II. Courses for M.Sc. in Chemistry
Semester I

Semester II

Basic Organic Chemistry PS452C (3 credits)

Advanced Organic ChemistryI PS456C (3 credits)

Basic Inorganic Chemistry PS453C (3 credits)

Advanced Inorganic ChemistryI PS457C (3 credits)

Quantum Chemistry PS454C (3 credits)

Molecular spectroscopy PS458C (3 credits)

Mathematical Methods for Chemists PS 455C (2 credits)  Concepts in Physical Chemistry PS459C (3 credits) 
Laboratory  I PS451C (6 credits)

Laboratory  II PS460C (6 credits)

Total Credits : 17

Total Credits : 18

Total Credits at the end of first year = 35  
Semester III

Semester IV

Advanced Organic ChemistryII PS462C (3 credits)

Supramolecular Chemistry PS615C (3 Credits)

Advanced Inorganic ChemistryII PS463C (3 credits)  Elective  I PS (3 credits) 
Analytical Techniques in Chemistry PS464C (3 credits)  Elective  II PS (3 credits) 
Computer Lab* PS461C (3 credits)  Research Project PS465C (7 credits) 
Research Project PS465C (7 credits)  
Total Credits : 19  Total Credits : 16 
Total Credits at the end of second year = 35 + 35 = 70 
*This course would be combined with the Computational Physics course (PS 427)
List of Elective Courses:
PS  Solid State Chemistry  PS614C  Advanced Spectroscopy and its Application 
PS613C  Computational Chemistry Applications  PS618C  Crystallography: Basic Principle and Applications 
PS  Biophysical Chemistry  PS  Natural Products and Medicinal Chemistry 
PS  Physical Organic Chemistry  PS616C  Molecular Materials 
Suggested elective courses from other schools/centers (list not exhaustive):
 Molecular Biology & Molecular Genetics (SBT)
 Free radicals and metal ions in biology and medicine (SCMM)
 Structural biology & Structure based drug design (SCMM)
 Biophysical Chemistry (SBT)
III. Courses for M.Sc. in Mathematics
Full details of all Mathematics courses can be found here.
Overview

Semester I 
Semester II 
Algebra I  Algebra II 
Complex Analysis  Measure Theory 
Real Analysis  Functional Analysis 
Basic Topology  Discrete Mathematics 
Semester III 
Semester IV 
Probability and Statistics  Partial Differential Equations 
Computational Mathematics  Elective I 
Ordinary Differential Equations  Elective II 
Project  Elective III 
Students can choose three elective courses from the ones which will be offered from the following list:
List of Elective Courses 

Number Theory  Differential Topology 
Harmonic Analysis  Analytic Number Theory 
Proofs  Advanced Algebra 
Algebraic Topology  Banach and Operator Algebras 
Full details of all Mathematics courses can be found here.