M. Sc. (Physics):Liquid Crystals:Advanced Quantum Mechanics

First Semester


Classical Mechanics
Statistical Mechanics
Quantum Mechanics
Mathematical Physics
Physics Lab I
Fundamentals of Computer Science and C Programming


Second Semester

Condensed Matter Physics
Experimental Techniques in Physics
Atomic and Molecular Physics
Electrodynamics
Electronics
Physics Lab II


Third Semester

Particle Physics
Nuclear Physics
Semiconductor Physics
Physics Lab III
Seminar


Fourth Semester

Dissertation


Advanced Quantum Mechanics

Relativistic Quantum Mechanics: Klein-Gordon equation, Dirac equation and its plane wave solutions, solution of Klein Gordan equation for a particle with coulomb potential, significance of negative energy solutions, spin angular momentum of the Dirac particle. The non-relativistic limit of Dirac equation, Electron in electromagnetic fields, spin magnetic moment, spin-orbit interaction, Dirac equation for a particle in a central field, fine structure of hydrogen atom, Lamb shift.

Field Quantization: Classical field theory, Lagrangian and Hamiltonian formalism of a particle in an electromagnetic field, Second quantization, Concepts and illustrations with Schrödinger field, Creation, annihilation and number operator.

Relativistic Quantum Field Theory: Quantization of a real scalar field and its application to one meson exchange potential. Quantization of a complex scalar field, Dirac field and e.m. field, Commutation relations, Covariant perturbation theory,

Interaction: Yukawa interaction, Coupling of electron and electromagnetic field, Global and guage invariance Feynman diagrams, Feynman rules, Feynman graphs for Compton and e-e scattering, Path integration method: Probability amplitude as path integral, action, free particle and harmonic oscillator motion, Wick's Theorem. Scattering matrix.