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Quantum Mechanics and Applications

Quantum Mechanics and Applications. Instructor: Professor Ajoy Ghatak, Department of Physics, IIT Delhi. 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 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-Gordan coefficients. Perturbation Theory with applications; The JWKB approximation with applications; Scattering Theory: Partial Wave Analysis. (from nptel.ac.in)

Lecture 13 - Linear Harmonic Oscillator (cont.)

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Module 01: Introduction and Basic Mathematical Preliminary

Lecture 01 - Basic Quantum Mechanics I: Wave Particle Duality

Lecture 02 - Basic Quantum Mechanics II: The Schrodinger Equation and the Dirac Delta Function

Lecture 03 - Dirac Delta Function and Fourier Transforms

Module 02: Simple Solutions of the One-dimensional Schrodinger Equation

Lecture 04 - The Free Particle

Lecture 05 - Physical Interpretation of The Wave Function

Lecture 06 - Expectation Values and The Uncertainty Principle

Lecture 07 - The Free Particle (Contd.)

Lecture 08 - Interference Experiment and The Particle in a Box Problem

Lecture 09 - On Eigenvalues and Eigenfunctions of the 1 Dimensional Schrodinger Equation

Module 03: Linear Harmonic Oscillator I

Lecture 10 - Linear Harmonic Oscillator

Lecture 11 - Linear Harmonic Oscillator (cont.)

Lecture 12 - Linear Harmonic Oscillator (cont.)

Lecture 13 - Linear Harmonic Oscillator (cont.)

Module 04: Simple Applications of Schrodinger Equation

Lecture 14 - Tunneling through a Barrier

Lecture 15 - The 1-Dimensional Potential Wall and Particle in a Box

Lecture 16 - Particle in a Box and Density of States

Module 05: Angular Momentum I

Lecture 17 - The Angular Momentum Problem

Lecture 18 - The Angular Momentum Problem (cont.)

Module 06: Hydrogen Atom and Other Two Body Problem

Lecture 19 - The Hydrogen Atom Problem

Lecture 20 - The Two Body Problem

Lecture 21 - The Two Body Problem: The Hydrogen atom, The Deuteron

Lecture 22 - Two Body Problem: The Diatomic Molecule (contd.), the 3 Dimensional Oscillator

Lecture 23 - 3d Oscillator and Dirac's Bra and Ket Algebra

Module 07: Bra-ket Algebra and Linear Harmonic Oscillator II

Lecture 24 - Dirac's Bra and Ket Algebra

Lecture 25 - Dirac's Bra and Ket Algebra: The Linear Harmonic Oscillator

Lecture 26 - The Linear Harmonic Oscillator using Bra and Ket Algebra (contd.)

Lecture 27 - The Linear Harmonic Oscillator: Coherent State

Lecture 28 - Coherent State and Relationship with the Classical Oscillator

Module 08: Angular Momentum II

Lecture 29 - Angular Momentum Problem using Operator Algebra

Lecture 30 - Angular Momentum Problem (contd.)

Lecture 31 - Pauli Spin Matrices and The Stern Gerlach Experiment

Lecture 32 - The Larmor Precession and NMR Spherical Harmonics using Operator Algebra

Lecture 33 - Addition of Angular Momentum: Clebsch-Gordan Coefficient

Lecture 34 - Clebsch-Gordan Coefficients

Module 09: The JWKB Approximations and Applications

Lecture 35 - The JWKB Approximation

Lecture 36 - The JWKB Approximation: Use of Connection Formulae to Solve Eigenvalue Problems

Lecture 37 - The JWKB Approximation: Use of Connection Formulae to Calculate Tunneling Probability

Lecture 38 - The JWKB Approximation: Tunneling Probability Calculations and Applications

Lecture 39 - The JWKB Approximation: Justification of the Connection Formulae

Module 10: Time Independent Perturbation Theory

Lecture 40 - Time Independent Perturbation Theory

Lecture 41 - Time Independent Perturbation Theory (cont.)

Lecture 42 - Time Independent Perturbation Theory (cont.)