Quantum Mechanics and Applications

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1 STUDENTS

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.

Course Curriculum

Basic Quantum Mechanics I: Wave Particle Duality Details 54:32
Basic Quantum Mechanics II: The Schrodinger Equation Details 58:59
Dirac Delta Function & Fourier Transforms Details 58:17
The Free Particle Details 50:24
Physical Interpretation of The Wave Function Details 58:6
Expectation Values & The Uncertainty Principle Details 1:3
The Free Particle (Contd.) Details 56:36
Interference Experiment & The Particle in a Box Problem Details 57:39
On Eigen Values and Eigen Functions of the 1 Dimensional.., Details 59:39
Linear Harmonic Oscillator Details 1:26
Linear Harmonic Oscillator (Contd1.) I Details 51:6
Linear Harmonic Oscillator (Contd2.) II Details 55:28
Linear Harmonic Oscillator (Contd3.) III Details 58:54
Tunneling through a Barrier Details 57:4
The 1-Dimensional Potential Wall & Particle in a Box Details 0:56
Particle in a Box and Density of States Details 54:37
The Angular Momentum Problem Details 57:53
The Angular Momentum Problem (Contd.) I Details 57:4
The Hydrogen Atom Problem Details 55:14
The Two Body Problem Details 57:9
TheTwo Body Problem: The Hydrogen atom, The Deutron Details 56:15
Two Body Problem: The Diatomic molecule (contd.) Details 55:49
3d Oscillator & Dirac’s Bra and Ket Algebra Details 56:17
Dirac’s Bra and Ket Algebra Details 56:40
Dirac’s Bra and Ket Algebra : The Linear Harmonic Oscillator Details 56:19
The Linear Harmonic Oscillator using Bra and Ket Algebra (contd.) Details 56:10
The Linear Harmonic Oscillator: Coherent State Details 48:21
Coherent State and Relationship with the Classical Oscillator Details 56:40
Angular Momentum Problem using Operator Algebra Details 55:17
Angular Momentum Problem (contd.) Details 57:45
Pauli Spin Matrices and The Stern Gerlach Experiment Details 55:9
The Larmor Precession and NMR Spherical Harmonics using Operator Algebra Details 57:24
Addition of Angular Momentum: Clebsch Gordon Coefficient Details 58:27
Clebsch Gordon Coefficients Details 56:44
The JWKB Approximation Details 57:33
The JWKB Approximation: Use of Connection Formulae to solve Eigen value Prob Details 56:43
The JWKB Approximation: Use of Connection Formulae Details 56:51
The JWKB Approximation: Tunneling Probability Calculations and Applications. Details 59:5
The JWKB Approximation: Justification of the Connection Formulae Details 58:21
Time Independent Perturbation Theory Details 56:20
Time Independent Perturbation Theory (Contd.1) Details 59:26
Time Independent Perturbation Theory (Contd.2) Details 57:31

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