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Quantum Mechanics and Applications

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Lecture 36: Mod-09 Lec-36 The JWKB Approximation: Use of Connection Formulae to solve Eigen value Prob

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Quantum Mechanics and Applications by Prof. Ajoy Ghatak, Department of Physics, IIT Delhi. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

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.

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  1. Mod-01 Lec-01 Basic Quantum Mechanics I: Wave Particle Duality
  2. Mod-01 Lec-02 Basic Quantum Mechanics II: The Schrodinger Equation
  3. Mod-01 Lec-03 Dirac Delta Function & Fourier Transforms
  4. Mod-02 Lec-04 The Free Particle
  5. Mod-02 Lec-05 Physical Interpretation of The Wave Function
  6. Mod-02 Lec-06 Expectation Values & The Uncertainty Principle
  7. Mod-02 Lec-07 The Free Particle (Contd.)
  8. Mod-02 Lec-08 Interference Experiment & The Particle in a Box Problem
  9. Mod-02 Lec-09 On Eigen Values and Eigen Functions of the 1 Dimensional..,
  10. Mod-03 Lec-10 Linear Harmonic Oscillator
  11. Mod-03 Lec-11 Linear Harmonic Oscillator (Contd1.)
  12. Mod-03 Lec-12 Linear Harmonic Oscillator (Contd2.)
  13. Mod-03 Lec-13 Linear Harmonic Oscillator (Contd3.)
  14. Mod-04 Lec-14 Tunneling through a Barrier
  15. Mod-04 Lec-15 The 1-Dimensional Potential Wall & Particle in a Box
  16. Mod-04 Lec-16 Particle in a Box and Density of States
  17. Mod-05 Lec-17 The Angular Momentum Problem
  18. Mod-05 Lec-18 The Angular Momentum Problem (Contd.)
  19. Mod-06 Lec-19 The Hydrogen Atom Problem
  20. Mod-06 Lec-20 The Two Body Problem
  21. Mod-06 Lec-21 TheTwo Body Problem: The Hydrogen atom, The Deutron
  22. Mod-06 Lec-22 Two Body Problem: The Diatomic molecule (contd.)
  23. Mod-06 Lec-23 3d Oscillator & Dirac's Bra and Ket Algebra
  24. Mod-07 Lec-24 Dirac's Bra and Ket Algebra
  25. Mod-07 Lec-25 Dirac's Bra and Ket Algebra : The Linear Harmonic Oscillator
  26. Mod-07 Lec-26 The Linear Harmonic Oscillator using Bra and Ket Algebra (contd.)
  27. Mod-07 Lec-27 The Linear Harmonic Oscillator: Coherent State
  28. Mod-07 Lec-28 Coherent State and Relationship with the Classical Oscillator
  29. Mod-08 Lec-29 Angular Momentum Problem using Operator Algebra
  30. Mod-08 Lec-30 Angular Momentum Problem (contd.)
  31. Mod-08 Lec-31 Pauli Spin Matrices and The Stern Gerlach Experiment
  32. Mod-08 Lec-32 The Larmor Precession and NMR Spherical Harmonics using Operator Algebra
  33. Mod-08 Lec-33 Addition of Angular Momentum: Clebsch Gordon Coefficient
  34. Mod-08 Lec-34 Clebsch Gordon Coefficients
  35. Mod-09 Lec-35 The JWKB Approximation
  36. Mod-09 Lec-36 The JWKB Approximation: Use of Connection Formulae to solve Eigen value Prob
  37. Mod-09 Lec-37 The JWKB Approximation: Use of Connection Formulae
  38. Mod-09 Lec-38 The JWKB Approximation: Tunneling Probability Calculations and Applications.
  39. Mod-09 Lec-39 The JWKB Approximation: Justification of the Connection Formulae
  40. Mod-10 Lec-40 Time Independent Perturbation Theory
  41. Mod-10 Lec-41 Time Independent Perturbation Theory (Contd.1)
  42. Mod-10 Lec-42 Time Independent Perturbation Theory (Contd.2)