Introductory Quantum Mechanics

Lectures

Week 1

1. Black Body Radiation I - Relevant Definitions and Black Body as cavity Video
2. Black Body Radiation II- Intensity of radiation in terms of energy density Video
3. Black Body Radiation III - Spectral energy density and radiation pressure inside a black body radiation Video
4. Black Body Radiation IV- Stephen's Boltzman law Video
5. Black Body Radiation V - Wein's Displacement law and analysis for spectral density Video
6. Black Body Radiation VI - Wein's distribution law and rayleigh - Jeans distribution law Video
7. Black Body Radiation VII - Quantum Hypothesis and plank's distribution Formula Video
8. Radiation as a collection of particles called photons Video
9. Quantum Hypothesis and specific heat of soilds Video
10. Bohr's Model of hydrogen spectrum Video

Week 2

11. Wilson Sommerfeld quantum condition I - Harmonic oscillator and particle in a box Video
12. Wilson Sommerfeld quantum condition II - Particle moving in a coulomb potential in a plane and related quantum numbers Video
13. Wilson Sommerfeld quantum condition III - Particle moving in a coulomb potential in 3D and related quantum numbers Video
14. Quantum conditions and atomic structure, electron spin and Pauli exclusion principle Video
15. Interaction of atoms with radiation : Eienstien's A and B coefficients Video
16. Stimulated emmision and amplification of light in a LASER Video
17. Brief description of a LASER Video

Week 3

18. Introduction to the correspondence principle Video
19. General nature of the correspondence principle Video
20. Selection rules (for transitions) through the correspondence principle Video
21. Applications of the correspondence principle : Einstiens A coefficient for the harmonic oscillator and the selection rules for atomic transitions Video
22. Heisenberg's formulations of quantum mechanics : expressing kinetic variables as matrices Video
23. Heisenberg's formulation of quantum mechanics : the quantum condition Video
24. Heisenberg's formulation of the quantum mechanics : Application to harmonic oscillator Video
25. Brief introduction to matrix mechanics and the quantum condition in matrix form Video

Week 4

26. Introduction to waves and wave equation Video
27. Sationary waves eigen values and eigen functions Video
28. Matter waves and their experimental detection Video
29. Represenating a moving paticle by a wave packet Video
30. Stationary-state Schrodinger equation and its solution for a particle in a box Video
31. Solution of the stationary-state Schrodinger equation for a simple harmonic oscillator Video

Week 5

32. Equivalance of Heisenberg and the Schrodinger formulations : Mathematical preliminaries Video
33. Equivalance of Heisenberg and Schrodinger formulations : The x and p operators and the quantum condition Video
34. Born interpretation of the wavefunction and expectation values of x and p operators Video
35. Uncertainty principle and its simple applications Video
36. Time dependent Schrodinger equation the probability current density and the continuity equation for the probability density Video
37. Ehrenfest theorem for the expectation values of x and p operators Video

Week 6

38. Solution of Schrodinger equation for a particle in one and two delta function potentials Video
39. Solution of Schrodinger equation for a particle in a finite well Video
40. Numerical solution of a one dimensional Schrodinger equation for bound states - I Video
41. Numerical solution of a one dimensional Schrodinger equation for bound states - II Video
42. Reflection and transmission of particles across a potential barrier Video
43. Quantum-tunneling and its examples Video

Week 7

44. Solution of the Schrodinger for free paticles and periodic boundary conditions Video
45. Electrons in a metal : Density of states and Fermi energy Video
46. Schrodinger equation for particles in spherically symmetric potential, angular momentum operator Video
47. Angular momentum operator and its eigenfunctions Video
48. Equation for radial component of the wavefunction in spherically symmteric potentials and general properties of its solution Video
49. Solution for radial component of the wavefunction for the hydrogen atom Video

Week 8

50. Numerical solution for the radial component of wavefunction for spherically symmetric potentials Video
51. Solution of the Schrodinger equation for one dimensional periodic potential : Bloch's theorem Video
52. Kroning-Penny model and energy bands Video
53. Kroning-Penny model with periodic Dirac delta function and energy bands Video
54. Discussion on bands Video
55. Summary of the course Video