**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

- Teacher: Sthitadhi Roy