Relativistic Quantum Mechanics of the Hydrogen Atom 
Relativistic Quantum Mechanics of the Hydrogen Atom
by IIT Madras / P. C. Deshmukh
Video Lecture 39 of 40
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Date Added: April 1, 2015

Lecture Description

This video lecture, part of the series Special Topics in Atomic Physics with Prof. Deshmukh by Prof. P. C. Deshmukh, does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Physics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,

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Course Index

  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

Course Description

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.

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