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NPTEL

Core - Quantum Mechanics and Applications

NPTEL and Indian Institute of Technology Delhi via YouTube

Overview

Instructor: Professor Ajoy Ghatak, Department of Physics, IIT Delhi.

In this course, you will learn 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 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.

Syllabus

Mod-01 Lec-01 Basic Quantum Mechanics I: Wave Particle Duality.
Mod-01 Lec-02 Basic Quantum Mechanics II: The Schrodinger Equation.
Mod-01 Lec-03 Dirac Delta Function & Fourier Transforms.
Mod-02 Lec-04 The Free Particle.
Mod-02 Lec-05 Physical Interpretation of The Wave Function.
Mod-02 Lec-06 Expectation Values & The Uncertainty Principle.
Mod-02 Lec-07 The Free Particle (Contd.).
Mod-02 Lec-08 Interference Experiment & The Particle in a Box Problem.
Mod-02 Lec-09 On Eigen Values and Eigen Functions of the 1 Dimensional..,.
Mod-03 Lec-10 Linear Harmonic Oscillator.
Mod-03 Lec-11 Linear Harmonic Oscillator (Contd1.).
Mod-03 Lec-12 Linear Harmonic Oscillator (Contd2.).
Mod-03 Lec-13 Linear Harmonic Oscillator (Contd3.).
Mod-04 Lec-14 Tunneling through a Barrier.
Mod-04 Lec-15 The 1-Dimensional Potential Wall & Particle in a Box.
Mod-04 Lec-16 Particle in a Box and Density of States.
Mod-05 Lec-17 The Angular Momentum Problem.
Mod-05 Lec-18 The Angular Momentum Problem (Contd.).
Mod-06 Lec-19 The Hydrogen Atom Problem.
Mod-06 Lec-20 The Two Body Problem.
Mod-06 Lec-21 TheTwo Body Problem: The Hydrogen atom, The Deutron.
Mod-06 Lec-22 Two Body Problem: The Diatomic molecule (contd.).
Mod-06 Lec-23 3d Oscillator & Dirac's Bra and Ket Algebra.
Mod-07 Lec-24 Dirac's Bra and Ket Algebra.
Mod-07 Lec-25 Dirac's Bra and Ket Algebra : The Linear Harmonic Oscillator.
Mod-07 Lec-26 The Linear Harmonic Oscillator using Bra and Ket Algebra (contd.).
Mod-07 Lec-27 The Linear Harmonic Oscillator: Coherent State.
Mod-07 Lec-28 Coherent State and Relationship with the Classical Oscillator.
Mod-08 Lec-29 Angular Momentum Problem using Operator Algebra.
Mod-08 Lec-30 Angular Momentum Problem (contd.).
Mod-08 Lec-31 Pauli Spin Matrices and The Stern Gerlach Experiment.
Mod-08 Lec-32 The Larmor Precession and NMR Spherical Harmonics using Operator Algebra.
Mod-08 Lec-33 Addition of Angular Momentum: Clebsch Gordon Coefficient.
Mod-08 Lec-34 Clebsch Gordon Coefficients.
Mod-09 Lec-35 The JWKB Approximation.
Mod-09 Lec-36 The JWKB Approximation: Use of Connection Formulae to solve Eigen value Prob.
Mod-09 Lec-37 The JWKB Approximation: Use of Connection Formulae.
Mod-09 Lec-38 The JWKB Approximation: Tunneling Probability Calculations and Applications..
Mod-09 Lec-39 The JWKB Approximation: Justification of the Connection Formulae.
Mod-10 Lec-40 Time Independent Perturbation Theory.
Mod-10 Lec-41 Time Independent Perturbation Theory (Contd.1).
Mod-10 Lec-42 Time Independent Perturbation Theory (Contd.2).

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