Instructor: Professor Ajoy Ghatak, Department of Physics, IIT Delhi.
In this course, you will learn Basic mathematical preliminaries: Dirac Delta function and Fourier Transforms. Wave-particle duality, one- and three-dimensional Schrodinger 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 Schrodinger 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 Schrodinger equation will also be discussed and 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-Gordan coefficients. Perturbation Theory with applications; The JWKB approximation with applications; Scattering Theory: Partial Wave Analysis.