Quantum Mechanics and Applications

Overview

Basic mathematical preliminaries:Dirac Delta function and Fourier Transforms.
Wave particle duality, one- and three- dimensional Schrdinger 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 Schrdinger 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 Schrdinger equation will also be discussed and a software to understand basic concepts in quantum mechanics will also be demonstrated).
Diracs 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.