Quantum Mechanics I

Overview

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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.

Syllabus

Mod-01 Lec-01 Quantum Mechanics -- An Introduction.
Mod-01 Lec-02 Linear Vector Spaces - I.
Mod-01 Lec-03 Linear Vector Spaces - II: The two-level atom.
Mod-01 Lec-04 Linear Vector Spaces - III: The three-level atom.
Mod-01 Lec-05 Postulates of Quantum Mechanics - I.
Mod-01 Lec-06 Postulates of Quantum Mechanics - II.
Mod-01 Lec-07 The Uncertainty Principle.
Mod-01 Lec-08 The Linear Harmonic Oscillator.
Mod-01 Lec-09 Introducing Quantum Optics.
Mod-01 Lec-10 An Interesting Quantum Superposition: The Coherent State.
Mod-01 Lec-11 The Displacement and Squeezing Operators.
Mod-01 Lec-12 Exercises in Finite Dimensional Linear Vector Spaces.
Mod-01 Lec-13 Exercises on Angular Momentum Operators and their algebra.
Mod-01 Lec-14 Exercises on Quantum Expectation Values.
Mod-01 Lec-15 Composite Systems.
Mod-01 Lec-16 The Quantum Beam Splitter.
Mod-01 Lec-17 Addition of Angular Momenta - I.
Mod-01 Lec-18 Addition of Angular Momenta - II.
Mod-01 Lec-19 Addition of Angular Momenta - III.
Mod-01 Lec-20 Infinite Dimensional Linear Vector Spaces.
Mod-01 Lec-21 Square-Integrable Functions.
Mod-01 Lec-22 Ingredients of Wave Mechanics.
Mod-01 Lec-23 The Schrodinger equation.
Mod-01 Lec-24 Wave Mechanics of the Simple Harmonic Oscillator.
Mod-01 Lec-25 One-Dimensional Square Well Potential: The Bound State Problem.
Mod-01 Lec-26 The Square Well and the Square Potential Barrier.
Mod-01 Lec-27 The Particle in a one-dimensional Box.
Mod-01 Lec-28 A Charged Particle in a Uniform Magnetic Field.
Mod-01 Lec-29 The Wavefunction: Its Single-valuedness and its Phase.
Mod-01 Lec-30 The Central Potential.
Mod-01 Lec-31 The Spherical Harmonics.
Mod-01 Lec-32 Central Potential: The Radial Equation.
Mod-01 Lec-33 Illustrative Exercises -I.
Mod-01 Lec-34 Illustrative Exercises -II.
Mod-01 Lec-35 Ehrenfest's Theorem.
Mod-01 Lec-36 Perturbation Theory - I.
Mod-01 Lec-37 Perturbation Theory - II.
Mod-01 Lec-38 Perturbation Theory - III.
Mod-01 Lec-39 Perturbation Theory - IV.
Mod-01 Lec-40 Time-dependent Hamiltonians.
Mod-01 Lec-41 The Jaynes-Cummings model.