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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)

Introduction


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

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Quantum Mechanics I
Instructor: Professor S. Lakshmi Bala, Department of Physics, IIT Madras. Syllabus. This course covers basic concepts of quantum mechanics and mathematical preliminaries.