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


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.)

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Quantum Mechanics and Applications
Instructor: Professor Ajoy Ghatak, Department of Physics, IIT Delhi. Syllabus. This course covers topics in quantum mechanics and its applications.