Foundation Courses

These courses are taken by all First year students across disciplines. Typically offered every semester, these courses run in multiple section.
The descriptions for these courses are given in the other section. The numbers in the last column refer the course units.

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 |

Physics Core Courses

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, Biot-Savart law, divergence & curl of magnetic field, magnetic vector potential, magnetic dipole; Magnetostatics in matter - magnetization and field of a magnetized object, the H-field, linear & non-linear 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, e-m 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 e-m fields and Poynting’s theorem, linear momentum and angular momentum of e-m 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 e-m fields, retarded potentials & Jefimenko's equations, Lienard-Weichert 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, Frank-Hertz experiment, Bohr-Sommerfeld 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, one-dimensional problems – potential wells, potential barriers, the harmonic oscillator; Hilbert space formalism – state vectors, Dirac’s bra-ket 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, Sturm-Liouville 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 QM-I) - operators and their
matrix representations, change of basis, position and momentum
representations, commuting and non-commuting 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,
Bose-Einstein and Fermi-Dirac 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, Bose-Einstein
condensation. | 3 |

PHY F313 | ## Computational Physics Review of programming language - C/C++, python, Matlab and
Mathematica; Functions and roots - Newton-Raphson method, rate of
convergence, system of algebraic equations; Numerical integration -
Romberg integration, Gaussian quadrature; Ordinary differential
equations - Euler Method, Runge-Kutta 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;
Monte-Carlo 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
tight-binding approximation; lattice vibration and thermal
properties; semiconductors - energy band gap in semiconductors,
carrier density of intrinsic and extrinsic semiconductors, the p-n
junction; magnetism - paramagnetism and diamagnetism, spontaneous
magnetism, magnetic ordering; super conductivity-basic 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, L-S
coupling and j-j coupling; Molecular structure - Born-Oppenheimer
approximation, rotation and vibration of diatomic and polyatomic
molecules, electronic structure and spin, rotational-vibrational and
electronic spectra of diatomic molecules, nuclear spin. | 3 |

PHY F343 | ## Nuclear and Particle Physics Bethe-Weizsacker 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,
Bohr-Wheeler theory, two-body problem, deuteron wave function with
central and non-central potential, electric quadrupole moment &
magnetic moment, exchange forces, low energy nucleon-nucleon
scattering, scattering length, effective range theory, spin
dependence of n-p 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 |

Electives

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 Milky-Way 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, space-time diagrams, Four vectors, tensors
in flat space-time, 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 psycho-acoustic
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,
wood-wind 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 ; hands-on work and
projects. | 3 |

PHY F317 | ## Introduction to Radio Astronomy Overview of Astronomy, Stellar and Galactic Astrophysics,
Bremsstrahlung, Synchrotron radiation, free-free radiation, and
Compton scattering, Radiative- transitions/line-emission, 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 : Q-switching, mode
locking, devices, techniques. Types of lasers : solid state lasers,
gas lasers, liquid lasers, semiconductor laser, x-ray laser, free
electron laser, maser. Non-linear 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 Klein-Gordon 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, Yang-Mills field, geometry of gauge fields, canonical
quantization of Klein-Gordon, Dirac and Electromagnetic field,
spontaneously broken gauge symmetries, Goldstone theorem,
superconductivity. | 4 |

PHY F413 | ## Particle Physics Klein-Gordon equation, time-dependent non-relativistic perturbation
theory, spinless electron-muon scattering and electron-positron
scattering, crossing symmetry, Dirac equation, standard examples of
scattering, parity violation and V-A 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 wave-equation, U(1)
local gauge invariance and QED, non-Abelian 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 space-time, 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-
Robertson-Walker (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, X-ray 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 zero-point energy, coherent states,
atom - field interaction - semiclassical and quantum, the Rabi
model, Jaynes-Cummings 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,
two-electron 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
fluctuation-dissipation theorem, critical exponents, calculation of
critical exponents, scale invariance, field driven transitions,
temperature driven condition, Landau-Ginzberg theory, two-point
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, Fokker-Planck
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, centre-fed
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 – Lienard-Wiechert potentials and fields, Larmor’s
formula and its relativistic generalization; Radiation damping –
radiative reaction force from conservation of energy,
Abraham-Lorentz model. | 4 |

PHY F426 | ## Physics of Semiconductor Devices Basics-Crystal structure, Wave Mechanics and the Schrodinger
Equation, Free and Bound Particles, Fermi energy, Fermi-Dirac
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, p-n junction, metal-semiconductor 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
3-tensors 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 spin-0 and spin-1/2, and super-symmetric
multiplet, introduction of spin-1, spin-2 and spin-3/2 through
appropriate local symmetries of spin-0 and spin-1/2 actions. | 3 |

PHY F433 | ## Topics in Non-linear 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 non-linear effects. The high
intensity laser-plasma interaction will cover processes of laser
light absorption in plasma at high and ultra-high intensities,
nonlinear processes in plasma, and light- matter interaction
processes at ultra-high 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, Hamilton-Jacobi Theory, Integrability and Action-Angle 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 Landau-Ginzburg (Mean Field Theory) theory for Second Order Phase Transitions, the Ising Model and some Examples, Phase Transitions as a symmetry-breaking 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, Non-perturbative 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, Tight-binding 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, H-Theorem; Postulate of statistical Mechanics; Temperature; Entropy; Microcanonical, Canonical, Grand-canonical ensembles - Derivation,calculation of macroscopic quantities, fluctuations, equivalence of ensembles, Applications, Ideal gases, Gibbs Paradox; Quantum mechanical ensemble theory; Bose-Einstein 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 1-d & 2-d; Liquid Helium, phase transitions and renormalization group. | 5 |

PHY G517 | ## Topics in Mathematical Physics Functions of complex variables, special functions, fourier analysis, sturm-Liuoville 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, electron-phonon 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 TheoryKlein-Gordon 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, Yang-Mills field, geometry of gauge fields, canonical quantization of Klein-Gordon, Dirac and Electromagnetic field, spontaneously broken gauge symmetries, Goldstone theorem, superconductivity. | 4 |

PHY F413 | ## Particle PhysicsKlein-Gordon equation, time-dependent non-relativistic perturbation theory, spinless electron-muon scattering and electron-positron scattering, crossing symmetry, Dirac equation, standard examples of scattering, parity violation and V-A 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 wave-equation, U(1) local gauge invariance and QED, non-Abelian 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 space-time, 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- Robertson-Walker (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 zero-point energy, coherent states, atom - field interaction - semiclassical and quantum, the Rabi model, Jaynes-Cummings 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, two-electron 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 fluctuation-dissipation theorem, critical exponents, calculation of critical exponents, scale invariance, field driven transitions, temperature driven condition, Landau-Ginzberg theory, two-point 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, Fokker-Planck 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, centre-fed 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 – Lienard-Wiechert potentials and fields, Larmor’s formula and its relativistic generalization; Radiation damping – radiative reaction force from conservation of energy, Abraham-Lorentz model. | 4 |

PHY F426 | ## Physics of Semiconductor DevicesBasics-Crystal structure, Wave Mechanics and the Schrodinger Equation, Free and Bound Particles, Fermi energy, Fermi-Dirac 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, p-n junction, metal-semiconductor 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 3-tensors 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 spin-0 and spin-1/2, and super-symmetric multiplet, introduction of spin-1, spin-2 and spin-3/2 through appropriate local symmetries of spin-0 and spin-1/2 actions. | 3 |