Course info

Class Timings: Mondays and Fridays from 11:00am - 12:30pm

Venue: Emmy Noether Seminar Room

First Meeting: 7 August 2023

Course Description: 

Hilbert and Fock spaces; second quantisation; symmetries and conservation laws; perturbation theory, correlation functions and scattering theory, basics of relativistic quantum mechanics, basics of path integrals (see below for further details of each topic) 

• Mathematical Preliminaries (4 lectures)
 – Review of vector spaces and quamtum mechanical states and operators
 – Introduction to Hilbert spaces and Fock spaces, and representations of many body  quantum states and operators therein
 – Introduction to second quantisation 

• Symmetries and quantum numbers (4 lectures)
– What and why of symmetries 
– Symmetries and conservation laws
– Examples with simple symmetries such as translation symmetry and linear momentum, rotational symmetry and angular momentum 

• Perturbation Theory (6 lectures) 
– Time-independent perturbation theory (non-degenerate and degenerate)
– Time-dependent perturbation theory 

• Correlation functions and Scattering (8 lectures)
– Introduction to Scattering Theory 
– Spin-1/2 Fermions – Bosons 

• Introduction to relativistic quantum mechanics (4 lectures)
– Klein Gordon Equation
– Dirac Equation and spin
– Spin-orbit and Zeeman coupling as relativistic corrections 

• Introduction to path-integrals (2 lectures)

References: 
• Principles of Quantum Mechanics by R. Shankar
• Modern Quantum Mechanics by J. J. Sakurai
• Advanced Quantum Mechanics by J. J. Sakurai
• Advanced Quantum Mechanics by F. Schawbl

Evaluation: Assignments 50% + End-Semester Examination (40%)+Impromptu class tests (10%).

Prerequisites: The students are expected to be familiar with the topics usually taught in first course in quantum mechanics. These include but are not limited to
• Wave-functions, uncertainty principle, superposition principle in context of quantum mechanics
• Schrodinger Equation • Free particles in dimensions, d = 1, 2, 3, · · ·
• Particle in a box in dimensions d = 1, 2, 3, · · ·
• One dimensional quantum harmonic oscillator

For more course detail: Link