1. Introductory lecture about this course
2. Quantum Mechanics and Symmetry of the Hydrogen Atom
3. Hydrogen atom: Rotational and Dynamical Symmetry of the 1/r Potential
4. Hydrogen atom: Dynamical Symmetry of the 1/r Potential
5. Degeneracy of the Hydrogen Atom: SO(4)
6. Wavefunctions of the Hydrogen Atom
7. Angular Momentum in Quantum Mechanics
8. Angular Momentum in Quantum Mechanics
9. Angular Momentum in Quantum Mechanics
10. Angular Momentum in Quantum Mechanics Dimensionality of the Direct
11. Angular Momentum in Quantum Mechanics CGC matrix
12. Angular Momentum in Quantum Mechanics - more on ITO, and the Wigner-Eckart Theorem
13. Angular Momentum in Quantum Mechanics Wigner-Eckart Theorem - 2
14. Hartree-Fock Self-Consistent Field formalism - 1
15. Hartree-Fock Self-Consistent Field formalism - 2
16. Hartree-Fock Self-Consistent Field formalism - 3
17. Hartree-Fock Self-Consistent Field formalism - 4
18. Hartree-Fock Self-Consistent Field formalism - 5
19. Perturbative treatment of relativistic effects... Schrodinger's and Dirac QM
20. Perturbative treatment of relativistic effects... Schrodinger's and Dirac QM
21. Probing the atom - Collisions and Spectroscopy - boundry conditions - 1
22. Atomic Probes - Collisions and Spectroscopy - boundry conditions - 2
23. Atomic Probes - Collisions and Spectroscopy
24. Atomic Probes - Time reversal symmetry
25. Atomic Photoionization cross sections, angular distributions of photoelectrons - 1
26. Atomic Photoionization cross sections, angular distributions of photoelectrons - 2
27. Atomic Photoionization cross sections, angular distributions of photoelectrons - 3
28. Atomic Photoionization cross sections, angular distributions of photoelectrons - 4
29. Atomic Photoionization cross sections
30. Stark- Zeeman Spectroscopy - Stark effect
31. Stark- Zeeman Spectroscopy
32. Stark- Zeeman Spectroscopy
33. Stark- Zeeman Spectroscopy - Anomalous Zeeman effect
34. Zeeman effect Fine structure, Hyperfine structure
35. Relativistic Quantum Mechanics of the Hydrogen Atom
36. Relativistic Quantum Mechanics of the Hydrogen Atom
37. Relativistic Quantum Mechanics of the Hydrogen Atom
38. Relativistic Quantum Mechanics of the Hydrogen Atom - 2
39. Relativistic Quantum Mechanics of the Hydrogen Atom
40. Relativistic Quantum Mechanics of the Hydrogen Atom - 1

The course will begin with the identification of a complete set of compatible observables for the non-relativistic Hydrogen atom, identify the complete set of 'good quantum numbers', discuss the associated constants of motion, and associated symmetries. The Laplace-Runge-Lenz vector and the Fock SO(4) symmetry of the Hydrogen atom will be discussed.
This will be followed by a discussion on coupling of Angular Momenta, Clebsch-Gordan Coefficients, Statement and Proof the Wigner-Eckart Theorem.
We shall then discuss the relativistic Hydrogen atom, Dirac equation. Foldy-Wouthuysen Transformation of Dirac Hamiltonian and Lamb shift.
Subsequently, the many-electron atom will be discussed to acquire an understanding of the Hartree-Fock Self-Consistent Field Formalism.
We shall then examine a Perturbative approach to relativistic effects; this would provide insight in the relativistic quantum mechanics discussed in an earlier unit based on the Dirac equation.
We shall then proceed to discuss methods to probe the atom. The methods are based on the alternative probes which use quantum collisions of atomic targets with probe particles and probing the atom with an electromagnetic field. We shall discuss the connections of these methods through the time-reversal symmetry and obtain the quantum solutions using appropriate boundary conditions. We shall obtain expressions for scattering cross sections, and also for photoionization cross-section and the angular distribution of the photoelectrons.
We shall then examine the quantum mechanics of atoms in external fields and study the Stark effect, and also the family of ZEEMAN effect spectroscopies. A brief introduction to the hyperfine structure and its applications in laser cooling of atoms, BEC, atomic clocks etc. will be pointed out.