Pre-requisites: B.Sc. Mathematics & Physics.
COURSE OUTLINE: You will learn,
Basic mathematical preliminaries: Dirac Delta function and Fourier Transforms. Wave-particle duality, one- and three-dimensional Schrödinger equation. The free particle problem in one dimension. Wave Packets and Group velocity. One-dimensional problems: Potential well of infinite and finite depths, the linear harmonic oscillator. Angular Momentum and rotation.
Three-dimensional Schrödinger equation: Particle in a box with applications to the free electron model. Particle in a spherically symmetric potential problem.
The hydrogen atom and the deuteron. (A numerical method to obtain solutions of the Schrödinger equation will also be discussed and a software to understand basic concepts in quantum mechanics will also be demonstrated).
Dirac’s bra - ket algebra; Linear Harmonic Oscillator problem using bra - ket algebra, creation and annihilation operators, transition to the classical oscillator, \coherent states.
The angular momentum problem, using bra - ket algebra, ladder operators and angular momentum matrices. The Stern Gerlach and magnetic resonance experiments. Addition of Angular Momenta and Clebsch Gordon coefficients.
Perturbation Theory with applications; The JWKB approximation with applications; Scattering Theory: Partial Wave Analysis.