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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. Onedimensional problems: Potential well of infinite and finite depths, the linear harmonic oscillator. Angular Momentum and rotation. Threedimensional 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 ClebschGordan 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 1Dimensional 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: ClebschGordan Coefficient Unlimited
 Lecture 34 – ClebschGordan 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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