Master of Science in Physics

Ordinary differential equations and Sturm-Liouville theory, partial differential equations and Green’s functions, functions of complex variables, Group theory, Calculus of Variations, Hamiltonian’s principle, Lagrangian and Hamiltonian dynamics.

Electrostatics, magneto-statics, time-varying fields and Maxwell's equations, Gauge transformations, Poynting's theorem and conservation laws, plane and guided waves, retarded potentials, radiation from accelerated charged particles; scattering.

Operators, state vectors, and the formal structure of quantum theory; operator treatments of simple systems; angular momentum and vector addition coefficients; stationary state perturbation theory; introduction to scattering theory for particles without spin, partial wave analysis, and Born approximation.

The main topics include: What is research, research in physics, research methodologies and resources, writing research proposals, technical writing and publication, presentation skills, critical reviewing of research work.

The statistical basis for thermodynamics; Review of classical statistical mechanics; Postulates of quantum statistical mechanics; Micro canonical ensemble; Grand canonical ensemble; Ideal Bose gas; phonon gas and Ideal Fermi gas.

The course covers the fundamental Physics concepts that help understand the electrical, optical and thermal properties of materials, Crystal lattices, Introduction to crystallography, Scattering of radiation, Lattice dynamics, Phonons and thermal Properties, Energy Bands in solids, Charge transport in metals and semiconductors.

Hadrons, Nuclear forces, Nuclear masses and nuclear sizes, nuclear quantum numbers, binding energy, Bethe-Weizsäcker semi-empirical mass formula, valley stability, element of quantum mechanics, angular momentum, Rutherford Scattering, forces between nucleons, the liquid drop model, the Fermi gas model, Shell model, magic numbers, liquid drop model, collective model, alpha decay, beta decay, gamma decay, nuclear reactions, quarks and leptons as basic constituents, particles and brief introduction of the standard model.

The student has to undertake a thorough literature review and formulate a proposal for a suitable research topic under the supervision of a faculty member.

The student has to undertake and complete a research topic under the supervision of a faculty member. The thesis work should provide the student with an in-depth perspective of a particular research problem in his chosen field of specialization. It is anticipated that the student be able to carry out his research fairly independently under the direction of his/her supervisor. The student is required to submit a final thesis documenting his research and defend his work in front of a committee.

Review of the Drude and the Sommerfeld models of metals and optical properties of solids. Plasmons, Polaritons, and Polarons. Superconductivity. Dielectrics and Ferroelectrics, Diamagnetism and Paramagnetism, Ferromagnetism and Antiferromagnetism, point defects, surface and interface physics, dislocations, Alloys.

Harmonic Oscillators and Phonons, Second Quantization for Particles, Electron-Phonon Interactions, Photons and Pair Distribution Function, Interaction Representation, S Matrix and Green’s functions, Wick's Theorem and Feynman Diagrams, Dyson's Equation and Rules for Constructing Diagrams, Matsubara, Retarded and Advanced Green's Functions, Linked Cluster Expansions and Real-Time Green's Functions, Kubo Formula for Electrical Conductivity, Independent Boson Models, Bethe Lattice and Tomonaga Model, Exchange and Correlation, Wigner Lattice.

Survey of computer hardware and software: Linux and object-oriented languages for scientific computing; Numerical methods for the solution of linear and nonlinear equations; Solutions of ordinary and partial differential equations with applications in physics systems, Oscillatory, Solar, random, statistical and mechanical; Monte Carlo methods with applications in statistical physics and phase transitions; Advanced computational techniques; First principles calculations.

Crystal Structure and Reciprocal Lattice, Electrons in a Periodic Potential, Models of Band Structure: Electrons and Holes, Density of States and Carrier Statistics, Carrier Transport, Phonons and Phonon Statistics, Scattering Processes, Excitons, Optical Absorption and Emission, Electroabsorption, Magnetoabsorption.

Radiative transitions in atoms. Quantum optics of photons. Photon statistics. Coherence and correlations. light-matter interactions in atomic and solid-state systems. Atom optics. Quantum computing and entangled states.

Theory of X-ray production and interaction process. X-ray sources, X-ray tubes' design and operation, synchrotron radiation facilities, Cosmic rays. X-ray collimators and detectors. Analytical techniques: Radiography, X-ray diffraction, X-ray fluorescence spectroscopy, X-ray photo emission spectroscopy, total x-ray reflection spectroscopy. Applications to bulk material, surfaces, interfaces and nano-materials.

Introduction to gauge theories and QED, electroweak interaction, experimental Tests of EW-theory, strong interaction and QCD, experimental Tests of QCD, flavor structure of the SM. Standard Model and its components, Symmetries, invariances, and conservation laws. The Standard Model of Particle Physics, Brout-Englert-Higgs mechanism, Higgs properties, high precision tests of the Standard Model at colliders, test of the Flavor Sector, searches for the new Physics Beyond the Standard Model (BSM), Physics at the Large Hadron Collider (LHC).

The formalism of quantum field theory, in particular: perturbation theory; Path integrals, Wick’s theorem; field quantisation; field-theoretical description of identical particles; Klein-Gordon equation; Lagrange formalism for fields; symmetries, Feynman diagrams, action variations, Noether's theorem, symmetries and conservation laws. Fields with spin; internal and spacetime symmetries; spin-1/2 particles; Dirac equation; spin-1 particles; gauge invariance; Quantum Electrodynamics, non-Abelian Gauge Theories, Lie Algebras; SU(n) groups. Quantum Chromodynamics; ghosts; propagators, and vertex functions, Feynman rules and diagrams, renormalization; ultraviolet divergences in the effective potential and in scattering amplitudes; dimensional regularization; loop diagrams; renormalization scheme dependence in perturbation theory.

Review of special relativity and Newtonian gravity; Gravity as geometry of curved spacetime; Geodesics and conservation laws; Schwarzschild geometry; Post-Newtonian expansions and tests of general relativity; Gravitational collapse and black holes; Linearized gravity and gravitational waves; Cosmological models for the expanding Universe.

The course would explore selected area(s) of Condensed Matter Physics that address the latest theories, discoveries and inventions. Selection of topics will be based on relevance and instructor’s preference.

The course would explore selected area(s) of High Energy Physics that address the latest theories, discoveries and inventions. Selection of topics will be based on relevance and instructor’s preference.