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Quantum Mechanics I

Quantum Mechanics I. Instructor: Professor S. Lakshmi Bala, Department of Physics, IIT Madras. This course covers basic concepts of quantum mechanics and mathematical preliminaries, eigenvalues, expectation values, measurement and the uncertainty principle, time evolution of wavepackets, 1-dimensional potential well problems, simple harmonic oscillator, central force problems, orbital angular momentum and spin, hydrogen atom, the Schrodinger and Heisenberg pictures, the interaction picture, the deuteron, invariance principles and conservation laws, charged particle in magnetic field, and elements of perturbation theory. (from nptel.ac.in)

Lecture 01 - Introduction

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Lecture 01 - Introduction

Lecture 02 - Linear Vector Spaces I

Lecture 03 - Linear Vector Spaces II: Two-Level Atom

Lecture 04 - Linear Vector Spaces III: The 3-Level Atom

Lecture 05 - Postulates of Quantum Mechanics I

Lecture 06 - Postulates of Quantum Mechanics II

Lecture 07 - The Uncertainty Principle

Lecture 08 - The Linear Harmonic Oscillator

Lecture 09 - Introducing Quantum Optics

Lecture 10 - An Interesting Quantum Superposition: The Coherent State

Lecture 11 - The Displacement and Squeezing Operators

Lecture 12 - Exercises in Finite Dimensional Linear Vector Spaces

Lecture 13 - Exercises on Angular Momentum Operators and Their Algebra

Lecture 14 - Exercises on Quantum Expectation Values

Lecture 15 - Composite Systems

Lecture 16 - The Quantum Beam Splitter

Lecture 17 - Addition of Angular Momenta I

Lecture 18 - Addition of Angular Momenta II

Lecture 19 - Addition of Angular Momenta III

Lecture 20 - Infinite Dimensional Linear Vector Spaces

Lecture 21 - Square-Integrable Functions

Lecture 22 - Ingredients of Wave Mechanics

Lecture 23 - The Schrodinger Equation

Lecture 24 - Wave Mechanics of the Simple Harmonic Oscillator

Lecture 25 - One-Dimensional Square Well Potential: The Bound State Problem

Lecture 26 - The Square Well and the Square Potential Barrier

Lecture 27 - The Particle in a One-dimensional Box

Lecture 28 - A Charged Particle in a Uniform Magnetic Field

Lecture 29 - The Wavefunction: Its Single-valuedness and its Phase

Lecture 30 - The Central Potential

Lecture 31 - The Spherical Harmonics

Lecture 32 - Central Potential: The Radial Equation

Lecture 33 - Illustrative Exercises I: Two Interacting Oscillators, Nonlinear Hamiltonians...

Lecture 34 - Illustrative Exercises II: Dynamics of a Particle in a Box, Harmonic Oscillator...

Lecture 35 - Ehrenfest's Theorem

Lecture 36 - Perturbation Theory I: Time-independent Hamiltonian, Perturbative Series...

Lecture 37 - Perturbation Theory II: Anharmonic Perturbation, Second-order Perturbation Theory

Lecture 38 - Perturbation Theory III: Non-degenerate First-order Perturbation ...

Lecture 39 - Perturbation Theory IV: Degenerate Perturbation, Hydrogen Atom ...

Lecture 40 - Time-dependent Hamiltonians

Lecture 41 - The Jaynes-Cummings Model