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Quantum Mechanics and Applications

Lecture 2: Basic Quantum Mechanics II: The Schrodinger Equation

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Lecture Details :

Quantum Mechanics and Applications by Prof. Ajoy Ghatak, Department of Physics, IIT Delhi. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

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.

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