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# Quantum Mechanics and Applications

### Overview

Pre-requisites: B.Sc. Mathematics & Physics.

COURSE OUTLINE: You will learn,

Basic mathematical preliminaries: Dirac Delta function and Fourier Transforms. Wave-particle duality, one- and three-dimensional Schrödinger 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 Schrödinger 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 Schrödinger 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 Clebsch Gordon 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).

Physics

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