PHY F111  Mechanics, Oscillations and WavesConservation Principles, Rotational Dynamics, Oscillations, Wave Motion, Reflection and Refraction, Interference, Diffraction, Polarisation.

3 
PHY F110 
Physics Laboratory (Mechanics, Oscillations and Waves

1 
The department also participates in offering  
BITS F111  Thermodynamics  3 
PHY F211 
Classical MechanicsReview of Newtonian mechanics, constraints and generalized coordinates, Lagrange’s equation of motion, calculus of variation and principle of least action, central force motion, kinematics of rigid body motion, rigid body equations of motion, heavy symmetrical top, Hamilton’s equations of motion, canonical transformations. 
4 
PHY F212 
Electromagnetic Theory IReview of mathematics  scalar and vector fields, calculus of scalar and vector fields in Cartesian and curvilinear coordinates, Dirac delta function; Electrostatics  electric field, divergence & curl of electric field, electric potential, work and energy in electrostatics, conductors, electric dipole; Electrostatics in Matter  polarization and field of a polarized object, electric displacement, linear dielectrics; Magnetostatics  Lorentz force law, BiotSavart law, divergence & curl of magnetic field, magnetic vector potential, magnetic dipole; Magnetostatics in matter  magnetization and field of a magnetized object, the Hfield, linear & nonlinear magnetic media; Electrodynamics  electromotive force, electromagnetic induction, Maxwell's equations in free space, planewave solutions of Maxwell’s equations in free space. 
3 
PHY F213 
Optical Physics and ApplicationsGeometrical optics  light as rays, Fermat’s principle, matrix methods in ray tracing; scalar wave theory of light, spatial and temporal coherence, theory of diffraction  Fresnel & Fraunhoffer diffraction, diffraction at rectangular and circular aperture, diffraction around opaque objects; crystal optics – electromagnetic wave propagation in anisotropic media, birefringence, em waves in nonlinear media, elements of nonlinear optics; scattering of light – Thomson and Rayleigh scattering; elements of modern optics  lasers and applications, holography, fiber optics, Fourier optics. 
3 
PHY F214  Physics Lab 2  Electromagnetism and optics  3 
PHY F241 
Electromagnetic Theory IIMaxwell's equations in matter, boundary conditions on electric and magnetic fields; energy of em fields and Poynting’s theorem, linear momentum and angular momentum of em fields, Maxwell's stress tensor; electromagnetic waves in dielectric media – reflection, refraction and transmission at interfaces; wave propagation in metals – absorption and dispersion; guided waves; potential formulation of em fields, retarded potentials & Jefimenko's equations, LienardWeichert potentials and fields of a moving point charge; dipole radiation & radiation due to point charges; special theory of relativity, relativistic mechanics, relativistic electrodynamics. 
4 
PHY F242 
Quantum Mechanics IOrigin of the quantum theory  black body radiation, photoelectric effect, Compton scattering, electron diffraction, Bohr model of hydrogen atom, FrankHertz experiment, BohrSommerfeld quantization condition; notion of wave function, statistical interpretation of the wave function, issues of normalization, the Heisenberg uncertainty relation; Schrodinger equation, stationary states and timeindependent Schrodinger equation, energy eigenvalues and eigenfunctions, onedimensional problems – potential wells, potential barriers, the harmonic oscillator; Hilbert space formalism – state vectors, Dirac’s braket notation, observables as Hermitian operators, eigenvalues and eigenstates of Hermitian operators, the measurement postulate. 
3 
PHY F243 
Methods of Mathematical PhysicsTensor analysis in Cartesian and curvilinear coordinates; linear vector spaces, linear transformations and theory of matrices; functions of a complex variable, contour integration and applications; elements of calculus of variation; series solution of ordinary differential equations, special functions, SturmLiouville theory; Fourier integral; partial differential equations of physics, solution of partial differential equations by separation of variables method, the Green function method. 
3 
PHY F244  Physics Lab 3  Modern Physics  3 
PHY F311 
Quantum Mechanics II
Hilbert space formalism (continued from QMI)  operators and their
matrix representations, change of basis, position and momentum
representations, commuting and noncommuting observables, the
generalized uncertainty relation; the time evolution operator and
Schrodinger equation, Schrodinger and Heisenberg picture, simple
harmonic oscillator using operator method; angular momentum
operators and their commutation relations, eigenvalues and
eigenvectors of angular momentum, spherically symmetric potentials,
the hydrogen atom; time independent perturbation theory, WKB
approximation, variational method; time dependent perturbation
theory, interaction of atom with classical radiation field;
identical particles.

3 
PHY F312 
Statistical Mechanics
Review of Thermodynamics  First and the second law of
thermodynamics, reversible and irreversible processes, entropy,
absolute temperature, thermodynamic potentials ; Statistical
description of macroscopic systems  micro and macro states, phase
space distribution, Liouville theorem, microcanonical ensemble,
statistical definition of temperature, pressure and entropy;
Canonical ensembles, probability distribution in canonical ensemble,
partition function and calculation of thermodynamic quantities,
equipartition and virial theorems, Maxwell velocity distribution,
paramgnetism, harmonic oscillators, polyatomic molecules; Grand
canonical ensembles  probability distribution in grand canonical
ensemble, grand partition function, calculation of thermodynamic
quantities; Quantum statistics  indistinguishable particles,
BoseEinstein and FermiDirac distribution, classical limit, photon
statistics, Planck distribution; Ideal Fermi gas  equation of state
of ideal Fermi gas, free electron gas in metals, Pauli
paramagnetism, Landau diamagnetism, statistical equilibrium of white
dwarf stars; Ideal Bose Gas  equation of state, BoseEinstein
condensation.

3 
PHY F313 
Computational Physics
Review of programming language  C/C++, python, Matlab and
Mathematica; Functions and roots  NewtonRaphson method, rate of
convergence, system of algebraic equations; Numerical integration 
Romberg integration, Gaussian quadrature; Ordinary differential
equations  Euler Method, RungeKutta method, predictor corrector
method, system of equations; Partial differential equations 
boundary value problems, finite difference method, finite element
method; discrete and fast Fourier transform; Eigenvalue problems;
MonteCarlo method  random numbers, sampling rules, metropolis
algorithm.

3 
PHY F341 
Solid State Physics
Crystal structure  direct and reciprocal lattice, Brillouin zone,
Xray diffraction and crystal structure; free electron theory of
metals; periodic potential and band theory of solids, the
tightbinding approximation; lattice vibration and thermal
properties; semiconductors  energy band gap in semiconductors,
carrier density of intrinsic and extrinsic semiconductors, the pn
junction; magnetism  paramagnetism and diamagnetism, spontaneous
magnetism, magnetic ordering; super conductivitybasic properties,
the London equation, elements of BCS theory.

3 
PHY F342 
Atomic and Molecular Physics
Interaction of electromagnetic field with atoms  transition rates,
dipole approximation, Einstein coefficients, selection rules and
spectrum of one electron atom, line intensities and shapes, line
widths and lifetimes; one electron atoms  fine and hyperfine
structure, interaction with external electric and magnetic fields;
two electron atoms  para and ortho states, level scheme, ground and
exited states of two electron atoms; many electron atoms  central
field approximation, Thomas –Fermi model, Hartree Fock method, LS
coupling and jj coupling; Molecular structure  BornOppenheimer
approximation, rotation and vibration of diatomic and polyatomic
molecules, electronic structure and spin, rotationalvibrational and
electronic spectra of diatomic molecules, nuclear spin.

3 
PHY F343 
Nuclear and Particle Physics
BetheWeizsacker mass formula, nuclear size, mirror nuclei, electric
multipole moments, Spherically and axially symmetric charge
distribution, electric quadrupole moment, nuclear magnetic moment,
nuclear decay, alpha and beta decay processes, nuclear fission,
BohrWheeler theory, twobody problem, deuteron wave function with
central and noncentral potential, electric quadrupole moment &
magnetic moment, exchange forces, low energy nucleonnucleon
scattering, scattering length, effective range theory, spin
dependence of np scattering, magic numbers, independent particle
model, collective model. Mesons and baryons, antiparticles,
neutrinos, strange particles, eightfold way, quark model,
intermediate vector bosons, four fundamental forces, basic vertices
and charactesitics of quantum electrodynamics, quantum flavordyamics
and quantum chromodynamics, decays and conservations laws, basic
ideas of standard model of particle physics, qualitative discussion
of current issues in particle physics.

3 
PHY F344  Physics Lab 4  Advanced Physics  3 
PHY F215 
Intro to Astronomy and Astrophysics
Introduction and scope, telescopes, distance and size measurements
of astronomical objects, celestial mechanics, the Sun, planets,
planet formation, interstellar medium, star formation, stellar
structure, stellar evolution, star clusters  open clusters,
globular clusters, the MilkyWay galaxy, nature of galaxies, normal
and active galaxies, Newtonian cosmology, cosmic microwave
background radiation, the early universe.

3 
PHY F315 
Theory of Relativity
Special theory of relativity : Experimental background and
postulates of the special theory, Lorentz transformation equations
and their implications, spacetime diagrams, Four vectors, tensors
in flat spacetime, relativistic kinematics and dynamics,
relativistic electromagnetism. General theory of relativity :
Principle of equivalence, gravitational red shift, geometry of
curved spacetime, Einstein field equation, spherically symmetric
solution of field equation.

3 
PHY F316 
Musical Acoustics
Mathematical description of sound waves; physical sound production
by vibrations in different dimensions; perception of music by the
human ear and brain, the scientific meaning of psychoacoustic
concepts of pitch, loudness and timbre; Fourier analysis as a tool
for characterizing timbre; musical scales, harmonics and tones;
musical instruments with plucked, bowed and struck strings,
woodwind instruments, reed instruments and the human voice,
percussions instruments such as tympani, and drums; engineering for
sound reproduction in transducers, mikes, amplifiers and
loudspeakers; sound spectrum analysis; basics of signal processing
for electronic music production, filtration and enhancement;
rudiments of room and auditorium acoustics ; handson work and
projects.

3 
PHY F317 
Introduction to Radio Astronomy
Overview of Astronomy, Stellar and Galactic Astrophysics,
Bremsstrahlung, Synchrotron radiation, freefree radiation, and
Compton scattering, Radiative transitions/lineemission, The radio
sky and sources of radio signals, Theory of statistical random
signals, Radio telescopes and Radio observations. Techniques of Line
and continuum observations, Pulsar observations. Radio telescopes,
antennas and receivers. Single dish and interferometric
observations, Beam patterns, aperture synthesis and deconvolution,
Phased arrays, Flux and Phase Calibration techniques. Study some
radio telescopes GMRT, VLA, OWFA.

3 
PHY F346 
Laser Science and Technology
Introduction to lasers, theory of radiation, laser basics, optical
resonators, longitudinal / transverse modes, pumping of laser media,
Line broadening mechanism, Transient behaviour : Qswitching, mode
locking, devices, techniques. Types of lasers : solid state lasers,
gas lasers, liquid lasers, semiconductor laser, xray laser, free
electron laser, maser. Nonlinear optics: Phase matching, second
harmonic generation, third harmonic generation, difference frequency
generation, optical parametric generation etc. Applications of
lasers : Industry, medicine, biology, optical /quantum
communication, thermonuclear fusion, isotope separation, holography,
laser cooling etc.

3 
PHY F412 
Intro to Quantum Field Theory
KleinGordon equation, SU(2) and rotation group, SL(2,C) and Lorentz
group, antiparticles, construction of Dirac spinors, algebra of
gamma matrices, Maxwell and Proca equations, Maxwell's equations and
differential geometry; Lagrangian Formulation of particle mechanics,
real scalar field and Noether's theorem, real and complex scalar
fields, YangMills field, geometry of gauge fields, canonical
quantization of KleinGordon, Dirac and Electromagnetic field,
spontaneously broken gauge symmetries, Goldstone theorem,
superconductivity.

4 
PHY F413 
Particle Physics
KleinGordon equation, timedependent nonrelativistic perturbation
theory, spinless electronmuon scattering and electronpositron
scattering, crossing symmetry, Dirac equation, standard examples of
scattering, parity violation and VA interaction, beta decay, muon
decay, weak neutral currents, Cabbibo angle, weak mixing angles, CP
violation, weak isospin and hypercharge, basic electroweak
interaction, Lagrangian and single particle waveequation, U(1)
local gauge invariance and QED, nonAbelian gauge invariance and
QCD, spontaneous symmetry breaking, Higgs mechanism, spontaneous
breaking of local SU(2) gauge symmetry.

4 
PHY F415 
General Theory of Relativity and Cosmology
Review of relativistic mechanics, gravity as geometry, descriptions
of curved spacetime, tensor analysis, geodesic equations, affine
connections, parallel transport, Riemann and Ricci tensors,
Einstein’s equations, Schwarzschild solution, classic tests of
general theory of relativity, mapping the universe, Friedmann
RobertsonWalker (FRW) cosmological model, Friedmann equation and
the evolution of the universe, thermal history of the early
universe, shortcomings of standard model of cosmology, theory of
inflation, cosmic microwave background radiations (CMBR),
baryogenesis, dark matter & dark energy.

3 
PHY F416 
Soft Condensed Matter
Forces, energies, timescale and dimensionality in soft condensed
matter, phase transition, mean field theory and its breakdown,
simulation of Ising spin using Monte Carlo and molecular dynamics,
colloidal dispersion, polymer physics, molecular order in soft
condensed matter – i) liquid crystals ii) polymer, supramolecular
self assembly.

4 
PHY F417 
Experimental Methods of Physics
Vacuum techniques, sample preparation techniques, Xray diffraction,
scanning probe microscopy, scanning electron microscopy, low
temperature techniques, magnetic measurements, Mossbauer and
positron annihilation spectroscopy, neutron diffraction, Rutherford
backscattering, techniques in nuclear experimentation, high energy
accelerators.

4 
PHY F419 
Advanced Solid State Physics
Schrodinger field theory (second quantized formalism), Bose and
Fermi fields, equivalence with many body quantum mechanics,
particles and holes, single particle Green functions and
propagators, diagrammatic techniques, application to Fermi systems
(electrons in a metal, electron – phonon interaction) and Bose
systems (superconductivity, superfluidity).

4 
PHY F420 
Quantum Optics
Quantization of the electromagnetic field, single mode and multimode
fields, vacuum fluctuations and zeropoint energy, coherent states,
atom  field interaction  semiclassical and quantum, the Rabi
model, JaynesCummings model, beam splitters and interferometry,
squeezed states, lasers.

4 
PHY F421 
Advanced Quantum Mechanics
Symmetries, conservation laws and degeneracies; Discrete symmetries
 parity, lattice translations and time reversal; Identical
particles, permutation symmetry, symmetrization postulate,
twoelectron system, the helium atom; Scattering theory  Lippman
Schwinger equation, Born approximation, optical theorem, eikonal
approximation, method of partial waves; Quantum theory of radiation
 quantization of electromagnetic field, interaction of
electromagnetic radiation with atoms; relativistic quantum mechanics

4 
PHY F422 
Group theory and Applications
Basic concepts – group axioms and examples of groups, subgroups,
cosets, invariant subgroups; group representation – unitary
representation, irreducible representation, character table, Schur’s
lemmas; the point symmetry group and applications to molecular and
crystal structure; Continuous groups – Lie groups, infinitesimal
transformation, structure constants; Lie algebras, irreducible
representations of Lie groups and Lie algebras; linear groups,
rotation groups, groups of the standard model of particle physics.

4 
PHY F423 
Special Topics in Statistical Mechanics
The Ising Model – Definition, equivalence to other models,
spontaneous magnetization, Bragg William approximation, Bethe
Peierls Approximation, one dimensional Ising model, exact solution
in one and two dimensions; Landau’s mean field theory for phase
transition – the order parameter, correlation function and
fluctuationdissipation theorem, critical exponents, calculation of
critical exponents, scale invariance, field driven transitions,
temperature driven condition, LandauGinzberg theory, twopoint
correlation function, Ginzberg criterion, Gaussian approximation;
Scaling hypothesis – universality and universality classes,
renormalization group; Elements of nonequilibrium statistical
mechanics – Brownian motion, diffusion and Langevin equation,
relation between dissipation and fluctuating force, FokkerPlanck
equation

4 
PHY F424 
Advanced Electrodynamics
Review of Maxwell’s equations – Maxwell’s equations, scalar and
vector potentials, gauge transformations of the potentials, the
electromagnetic wave equation, retarded and advanced Green’s
functions for the wave equation and their interpretation,
transformation properties of electromagnetic fields; Radiating
systems – multipole expansion of radiation fields, energy and
angular momentum of multipole radiation, multipole radiation in
atoms and nuclei, multipole radiation from a linear, centrefed
antenna; Scattering and diffraction – perturbation theory of
scattering, scattering by gases and liquids, scattering of EM waves
by a sphere, scalar and vector diffraction theory, diffraction by a
circular aperture; Dynamics of relativistic particles and EM fields
– Lagrangian of a relativistic charged particle in an EM field,
motion in uniform, static electromagnetic fields, Lagrangian of the
EM fields, solution of wave equation in covariant form, invariant
Green’s functions; Collisions, energy loss and scattering of a
charged particle, Cherenkov radiation, the Bremsstrahlung; Radiation
by moving charges – LienardWiechert potentials and fields, Larmor’s
formula and its relativistic generalization; Radiation damping –
radiative reaction force from conservation of energy,
AbrahamLorentz model.

4 
PHY F426 
Physics of Semiconductor Devices
BasicsCrystal structure, Wave Mechanics and the Schrodinger
Equation, Free and Bound Particles, Fermi energy, FermiDirac
Statistics, Fermi level, Density of states, Band Theory of Solids,
Concept of Band Gap, direct and indirect band gap, equation of
motion, electron effective mass, concept of holes, Doping in
semiconductors, Carrier transport  transport equations, Generation
/ Recombination Phenomena, Semiconductor processing and
characterization, pn junction, metalsemiconductor contacts, MOS
capacitors, JFET, MESFET, MOSFET, Heterojunction devices, Quantum
effect, nanostructures, Semiconductor and Spin Physics, Magnetic
Semiconductors

4 
PHY F428 
Quantum Information Theory
Classical Information, probability and information measures, methods
of open quantum systems using density operator formalism, quantum
operations, Kraus operators. Measurement and information, Entropy
and information, data compression, channel capacity, Resource theory
of quantum correlations and coherence, and some current issues.

3 
PHY F431 
Geometric Methods in Physics
Manifolds, tensors, differential forms and examples from Physics,
Riemannian geometry, relevance of topology to Physics, integration
on a manifold, Gauss theorem and Stokes’ theorem using integrals of
differential forms, fibre bundles and connections, applications of
geometrical methods in Classical and Quantum Mechanics,
Electrodynamics, Gravitation, and Quantum field theory. Rotations in
real complex and Minkowski spaces laying group theoretical basis of
3tensors and 4 tensors and spinors, transition from a discrete to
continuous system, stress energy tensor, relativistic field theory,
Noether’s theorem, tensor and spinor fields as representation of
Lorentz group, action for spin0 and spin1/2, and supersymmetric
multiplet, introduction of spin1, spin2 and spin3/2 through
appropriate local symmetries of spin0 and spin1/2 actions.

3 
PHY F433 
Topics in Nonlinear Optics
In this course, the nonlinear processes which take place during the
interaction of light with matter will be studied in medium intensity
(10 3 to 10 8 W/cm 2 ) to high and ultra high intensity (10 9 to 10
21 W/cm 2 ) regimes. The nonlinear optics in the medium intensity
regime in dielectric materials will cover basic concepts of
nonlinear susceptibility, phase matching etc. and will discuss all
major second order and third order nonlinear effects. The high
intensity laserplasma interaction will cover processes of laser
light absorption in plasma at high and ultrahigh intensities,
nonlinear processes in plasma, and light matter interaction
processes at ultrahigh intensities. After studying the nonlinear
physical processes happening in these intensity regions, four useful
applications in four intensity regimes will be discussed.

3 
Course Number  Course title and Syllabus  Units 
PHY G511  Theoretical Physics Calculus of Variations and its applications to Lagrangian and Hamiltonian Dynamics, Thermodynamics and Geometric Optics and Electrodynamics. Geometric and Group theoretic foundations of Hamiltonian Dynamics, HamiltonJacobi Theory, Integrability and ActionAngle Variables, Adiabatic Invariants, Transformation (Lie) Groups and Classical Mechanics. Modern Theory of Phase Transitions and Critical Phenomenon: Thermodynamics and Statistical Mechanics of Phase Transitions, General Properties (eg Scaling, Universality, Critical exponents) and Order of Phase Transitions; Introduction to LandauGinzburg (Mean Field Theory) theory for Second Order Phase Transitions, the Ising Model and some Examples, Phase Transitions as a symmetrybreaking phenomenon.

5 
PHY G512  Advanced Quantum Field Theory Diagrammatics : Feynman diagrams & rules, Loop diagrams, Smatrix, Path integrals, Gauge theories, QED and QCD Lagrangians, Renormalization group, Nonperturbative states.

5 
PHY G513  Classical Electrodynamics Review of Electrostatics, Magnetostatics, and solution of Boundary Value Problems. Method of Images. Maxwell equations for time dependent fields, Propagation of electromagnetic waves in unbounded media. Waveguides & Cavity Resonators. Absorption, Scattering and Diffraction, Special Relativity, Covariant formulation of Classical Electrodynamics. Dynamics of charged particles in electromagnetic fields. Radiation by moving charges and Cerenkov Radiation.

5 
PHY G514  Quantum Theory and Applications Mathematics of linear vector spaces, Postulates of Quantum Mechanics, Review of exactly solvable bound state problems, WKB methods, Angular momentum, Spin, Addition of angular momenta, Systems with many degrees of freedom, Perturbation theory, Scattering theory, Dirac equation.

5 
PHY G515  Condensed Matter Physics Free electron models, Reciprocal lattice, Electrons in weak periodic potential, Tightbinding method, Semiclassical model of electron dynamics, Theory of conduction in metals, Theory of harmonic crystals, Anharmonic effects, Semiconductors, Diamagnetism and paramagnetism, Superconductivity.

5 
PHY G516  Statistical Physics and Applications</span > Liouville’s theorem, Boltzmann transport equation, HTheorem; Postulate of statistical Mechanics; Temperature; Entropy; Microcanonical, Canonical, Grandcanonical ensembles  Derivation,calculation of macroscopic quantities, fluctuations, equivalence of ensembles, Applications, Ideal gases, Gibbs Paradox; Quantum mechanical ensemble theory; BoseEinstein statistics – derivation, Bose Einstein condensation, applications; Fermi Dirac Statistics – derivation, applications  Equation of state of ideal Fermi gas, Landau Diamagnetism, etc; Radiation; Maxwell Boltzmann statistics; Interacting systems – cluster expansion, Ising model in 1d & 2d; Liquid Helium, phase transitions and renormalization group.

5 
PHY G517  Topics in Mathematical Physics Functions of complex variables, special functions, fourier analysis, sturmLiuoville theory, partial differential equation with examples, Greens functions, Group theory, differential forms, approximation methods in solutions of PDE’s, vector valued PDE’s.

5 
PHY G521  Nuclear and Particle Physics 
5 
PHY G531  Selected Topics in Solid State Physics</span > Schrodinger Field Theory (2nd Quantized formalism), Bose and Fermi fields, equivalence with many body quantum mechanics, particles and holes, Single particle Green functions and propagators, Diagrammatic techniques, Application to Fermi systems electrons in a metal, electronphonon interaction) and Bose systems (superconductivity, superfluidity).

5 
PHY G541  Physics of Semiconductor Devices Electrons and Phonons in Crystals; Carrier dynamics in semiconductors; Junctions in semiconductors (including metals and insulators); Heterostructures; Quantum wells and Lowdimensional systems; Tunnelling transport; Optoelectronics properties; Electric and magnetic fields; The 2d Electron gas; Semiconductor spintronic devices

5 
SKILL G641  Modern Experimental Methods  5 
BITS G513  Studies in Advanced Topics  5 
BITS G649  Reading Course  5 
BITS G529  Research Project 1  5 
BITS G539  Research Project 2  5 
SKILL G661  Research Methodology  5 
PHY F412  Intro to Quantum Field TheoryKleinGordon equation, SU(2) and rotation group, SL(2,C) and Lorentz group, antiparticles, construction of Dirac spinors, algebra of gamma matrices, Maxwell and Proca equations, Maxwell's equations and differential geometry; Lagrangian Formulation of particle mechanics, real scalar field and Noether's theorem, real and complex scalar fields, YangMills field, geometry of gauge fields, canonical quantization of KleinGordon, Dirac and Electromagnetic field, spontaneously broken gauge symmetries, Goldstone theorem, superconductivity.

4 
PHY F413  Particle PhysicsKleinGordon equation, timedependent nonrelativistic perturbation theory, spinless electronmuon scattering and electronpositron scattering, crossing symmetry, Dirac equation, standard examples of scattering, parity violation and VA interaction, beta decay, muon decay, weak neutral currents, Cabbibo angle, weak mixing angles, CP violation, weak isospin and hypercharge, basic electroweak interaction, Lagrangian and single particle waveequation, U(1) local gauge invariance and QED, nonAbelian gauge invariance and QCD, spontaneous symmetry breaking, Higgs mechanism, spontaneous breaking of local SU(2) gauge symmetry.

4 
PHY F415  General Theory of Relativity and Cosmology</span >Review of relativistic mechanics, gravity as geometry, descriptions of curved spacetime, tensor analysis, geodesic equations, affine connections, parallel transport, Riemann and Ricci tensors, Einstein’s equations, Schwarzschild solution, classic tests of general theory of relativity, mapping the universe, Friedmann RobertsonWalker (FRW) cosmological model, Friedmann equation and the evolution of the universe, thermal history of the early universe, shortcomings of standard model of cosmology, theory of inflation, cosmic microwave background radiations (CMBR), baryogenesis, dark matter & dark energy.

3 
PHY F416  Soft Condensed MatterForces, energies, timescale and dimensionality in soft condensed matter, phase transition, mean field theory and its breakdown, simulation of Ising spin using Monte Carlo and molecular dynamics, colloidal dispersion, polymer physics, molecular order in soft condensed matter – i) liquid crystals ii) polymer, supramolecular self assembly.

4 
PHY F419  Advanced Solid State PhysicsSchrodinger field theory (second quantized formalism), Bose and Fermi fields, equivalence with many body quantum mechanics, particles and holes, single particle Green functions and propagators, diagrammatic techniques, application to Fermi systems (electrons in a metal, electron – phonon interaction) and Bose systems (superconductivity, superfluidity).

4 
PHY F420  Quantum OpticsQuantization of the electromagnetic field, single mode and multimode fields, vacuum fluctuations and zeropoint energy, coherent states, atom  field interaction  semiclassical and quantum, the Rabi model, JaynesCummings model, beam splitters and interferometry, squeezed states, lasers.

4 
PHY F421  Advanced Quantum MechanicsSymmetries, conservation laws and degeneracies; Discrete symmetries  parity, lattice translations and time reversal; Identical particles, permutation symmetry, symmetrization postulate, twoelectron system, the helium atom; Scattering theory  Lippman Schwinger equation, Born approximation, optical theorem, eikonal approximation, method of partial waves; Quantum theory of radiation  quantization of electromagnetic field, interaction of electromagnetic radiation with atoms; relativistic quantum mechanics

4 
PHY F422  Group theory and ApplicationsBasic concepts – group axioms and examples of groups, subgroups, cosets, invariant subgroups; group representation – unitary representation, irreducible representation, character table, Schur’s lemmas; the point symmetry group and applications to molecular and crystal structure; Continuous groups – Lie groups, infinitesimal transformation, structure constants; Lie algebras, irreducible representations of Lie groups and Lie algebras; linear groups, rotation groups, groups of the standard model of particle physics.

4 
PHY F423  Special Topics in Statistical Mechanics</span >The Ising Model – Definition, equivalence to other models, spontaneous magnetization, Bragg William approximation, Bethe Peierls Approximation, one dimensional Ising model, exact solution in one and two dimensions; Landau’s mean field theory for phase transition – the order parameter, correlation function and fluctuationdissipation theorem, critical exponents, calculation of critical exponents, scale invariance, field driven transitions, temperature driven condition, LandauGinzberg theory, twopoint correlation function, Ginzberg criterion, Gaussian approximation; Scaling hypothesis – universality and universality classes, renormalization group; Elements of nonequilibrium statistical mechanics – Brownian motion, diffusion and Langevin equation, relation between dissipation and fluctuating force, FokkerPlanck equation

4 
PHY F424  Advanced ElectrodynamicsReview of Maxwell’s equations – Maxwell’s equations, scalar and vector potentials, gauge transformations of the potentials, the electromagnetic wave equation, retarded and advanced Green’s functions for the wave equation and their interpretation, transformation properties of electromagnetic fields; Radiating systems – multipole expansion of radiation fields, energy and angular momentum of multipole radiation, multipole radiation in atoms and nuclei, multipole radiation from a linear, centrefed antenna; Scattering and diffraction – perturbation theory of scattering, scattering by gases and liquids, scattering of EM waves by a sphere, scalar and vector diffraction theory, diffraction by a circular aperture; Dynamics of relativistic particles and EM fields – Lagrangian of a relativistic charged particle in an EM field, motion in uniform, static electromagnetic fields, Lagrangian of the EM fields, solution of wave equation in covariant form, invariant Green’s functions; Collisions, energy loss and scattering of a charged particle, Cherenkov radiation, the Bremsstrahlung; Radiation by moving charges – LienardWiechert potentials and fields, Larmor’s formula and its relativistic generalization; Radiation damping – radiative reaction force from conservation of energy, AbrahamLorentz model.

4 
PHY F426  Physics of Semiconductor DevicesBasicsCrystal structure, Wave Mechanics and the Schrodinger Equation, Free and Bound Particles, Fermi energy, FermiDirac Statistics, Fermi level, Density of states, Band Theory of Solids, Concept of Band Gap, direct and indirect band gap, equation of motion, electron effective mass, concept of holes, Doping in semiconductors, Carrier transport  transport equations, Generation / Recombination Phenomena, Semiconductor processing and characterization, pn junction, metalsemiconductor contacts, MOS capacitors, JFET, MESFET, MOSFET, Heterojunction devices, Quantum effect, nanostructures, Semiconductor and Spin Physics, Magnetic Semiconductors

4 
PHY F428  Quantum Information TheoryClassical Information, probability and information measures, methods of open quantum systems using density operator formalism, quantum operations, Kraus operators. Measurement and information, Entropy and information, data compression, channel capacity, Resource theory of quantum correlations and coherence, and some current issues.

3 
PHY F431  Geometric Methods in PhysicsManifolds, tensors, differential forms and examples from Physics, Riemannian geometry, relevance of topology to Physics, integration on a manifold, Gauss theorem and Stokes’ theorem using integrals of differential forms, fibre bundles and connections, applications of geometrical methods in Classical and Quantum Mechanics, Electrodynamics, Gravitation, and Quantum field theory. Rotations in real complex and Minkowski spaces laying group theoretical basis of 3tensors and 4 tensors and spinors, transition from a discrete to continuous system, stress energy tensor, relativistic field theory, Noether’s theorem, tensor and spinor fields as representation of Lorentz group, action for spin0 and spin1/2, and supersymmetric multiplet, introduction of spin1, spin2 and spin3/2 through appropriate local symmetries of spin0 and spin1/2 actions.

3 