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September 23, 2023

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Description

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)

Course Curriculum

    • Lecture 01 – Basic Quantum Mechanics I: Wave Particle Duality Unlimited
    • Lecture 02 – Basic Quantum Mechanics II: The Schrodinger Equation and the Dirac Delta Function Unlimited
    • Lecture 03 – Dirac Delta Function and Fourier Transforms Unlimited
    • Lecture 04 – The Free Particle Unlimited
    • Lecture 05 – Physical Interpretation of The Wave Function Unlimited
    • Lecture 07 – The Free Particle (Contd.) Unlimited
    • Lecture 08 – Interference Experiment and The Particle in a Box Problem Unlimited
    • Lecture 09 – On Eigenvalues and Eigenfunctions of the 1 Dimensional Schrodinger Equation Unlimited
    • Lecture 10 – Linear Harmonic Oscillator Unlimited
    • Lecture 11 – Linear Harmonic Oscillator (cont.) Unlimited
    • Lecture 12 – Linear Harmonic Oscillator (cont.) Unlimited
    • Lecture 13 – Linear Harmonic Oscillator (cont.) Unlimited
    • Lecture 14 – Tunneling through a Barrier Unlimited
    • Lecture 15 – The 1-Dimensional Potential Wall and Particle in a Box Unlimited
    • Lecture 16 – Particle in a Box and Density of States Unlimited
    • Lecture 17 – The Angular Momentum Problem Unlimited
    • Lecture 18 – The Angular Momentum Problem (cont.) Unlimited
    • Lecture 19 – The Hydrogen Atom Problem Unlimited
    • Lecture 20 – The Two Body Problem Unlimited
    • Lecture 21 – The Two Body Problem: The Hydrogen atom, The Deuteron Unlimited
    • Lecture 22 – Two Body Problem: The Diatomic Molecule (contd.), the 3 Dimensional Oscillator Unlimited
    • Lecture 23 – 3d Oscillator and Dirac’s Bra and Ket Algebra Unlimited
    • Lecture 24 – Dirac’s Bra and Ket Algebra Unlimited
    • Lecture 25 – Dirac’s Bra and Ket Algebra: The Linear Harmonic Oscillator Unlimited
    • Lecture 26 – The Linear Harmonic Oscillator using Bra and Ket Algebra (contd.) Unlimited
    • Lecture 27 – The Linear Harmonic Oscillator: Coherent State Unlimited
    • Lecture 28 – Coherent State and Relationship with the Classical Oscillator Unlimited
    • Lecture 29 – Angular Momentum Problem using Operator Algebra Unlimited
    • Lecture 30 – Angular Momentum Problem (contd.) Unlimited
    • Lecture 31 – Pauli Spin Matrices and The Stern Gerlach Experiment Unlimited
    • Lecture 32 – The Larmor Precession and NMR Spherical Harmonics using Operator Algebra Unlimited
    • Lecture 33 – Addition of Angular Momentum: Clebsch-Gordan Coefficient Unlimited
    • Lecture 34 – Clebsch-Gordan Coefficients Unlimited
    • Lecture 35 – The JWKB Approximation Unlimited
    • Lecture 36 – The JWKB Approximation: Use of Connection Formulae to Solve Eigenvalue Problems Unlimited
    • Lecture 37 – The JWKB Approximation: Use of Connection Formulae to Calculate Tunneling Probability Unlimited
    • Lecture 38 – The JWKB Approximation: Tunneling Probability Calculations and Applications Unlimited
    • Lecture 39 – The JWKB Approximation: Justification of the Connection Formulae Unlimited
    • Lecture 40 – Time Independent Perturbation Theory Unlimited
    • Lecture 41 – Time Independent Perturbation Theory (cont.) Unlimited
    • Lecture 42 – Time Independent Perturbation Theory (cont.) Unlimited

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