Quantum Mechanics and the Symmetry of the hydrogen atom – Complete set of observables for the non-relativistic Hydrogen atom – radial and angular wavefunctions; Complete set of ‘good quantum numbers – associated constants of motion and associated symmetries. The Laplace-Runge-Lenz vector and the Fock SO(4) symmetry of the Hydrogen atom – Coupling of Angular Momenta, Clebsch-Gordan Coefficients, Statement and Proof the Wigner-Eckart – Relativistic Hydrogen Atom. Foldy-Wouthuysen Transformation of Dirac Hamiltonian – Identical Particles; Exchange interaction and N-electron systems. The Hartree-Fock Self-Consistent Field Formalism. Koopmans Theorem – Perturbative analysis of relativistic interactions in atoms – Probing the atom – quantum collisions and photoabsorption processes – Photoionization cross-section and angular distribution of the photoelectrons – Effects of applied electromagnetic fields. Stark effect. Zeeman effect (normal and anomalous) in atomic spectroscopy, Paschen-Back effect. Hyperfine structure. Introduction to laser cooling of atoms and Bose-Einstein condensation.

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Course Curriculum

Introductory lecture about this course Details 43:6
Quantum Mechanics and Symmetry of the Hydrogen Atom Details 46:39
Hydrogen atom: Rotational and Dynamical Symmetry of the 1/r Potential Details 50:1
Hydrogen atom: Dynamical Symmetry of the 1/r Potential I Details 55:14
Degeneracy of the Hydrogen Atom: SO(4) Details 51:11
Wavefunctions of the Hydrogen Atom Details 1:1:12
Angular Momentum in Quantum Mechanics Details
Angular Momentum in Quantum Mechanics I Details
Angular Momentum in Quantum Mechanics II Details 41:44
Angular Momentum in Quantum Mechanics Dimensionality of the Direct III Details 49:10
Angular Momentum in Quantum Mechanics CGC matrix IV Details 47:47
Angular Momentum in Quantum Mechanics – more on ITO, and the Wigner-Eckart Theorem V Details 46:15
Angular Momentum in Quantum Mechanics Wigner-Eckart Theorem VI Details 43:37
Relativistic Quantum Mechanics of the Hydrogen Atom – 1 Details
Relativistic Quantum Mechanics of the Hydrogen Atom I Details
Relativistic Quantum Mechanics of the Hydrogen Atom II Details
Relativistic Quantum Mechanics of the Hydrogen Atom III Details
Relativistic Quantum Mechanics of the Hydrogen Atom IV Details
Relativistic Quantum Mechanics of the Hydrogen Atom V Details
Hartree-Fock Self-Consistent Field formalism – 1 Details 53:42
Hartree-Fock Self-Consistent Field formalism – I Details 57:52
Hartree-Fock Self-Consistent Field formalism – 3 Details 46:56
Hartree-Fock Self-Consistent Field formalism – II Details 49:36
Hartree-Fock Self-Consistent Field formalism – III Details 1:2:46
Perturbative treatment of relativistic effects… Schrodinger’s and Dirac QM Details 41:34
Perturbative treatment of relativistic effects… Schrodinger’s and Dirac QM II Details 47:15
Probing the atom – Collisions and Spectroscopy – boundry conditions – 1 Details
Atomic Probes – Collisions and Spectroscopy – boundry conditions Details 52:51
Atomic Probes – Collisions and Spectroscopy I Details 50:34
Atomic Probes – Time reversal symmetry II Details 48:13
Atomic Photoionization cross sections, angular distributions of photoelectrons III Details 0:37
Atomic Photoionization cross sections, angular distributions of photoelectrons IV Details 59:23
Atomic Photoionization cross sections, angular distributions of photoelectrons V Details 39:1
Atomic Photoionization cross sections, angular distributions of photoelectrons VI Details 43:19
Atomic Photoionization cross sections VII Details 50:51
Stark- Zeeman Spectroscopy – Stark effect Details 49:40
Stark- Zeeman Spectroscopy I Details 46:18
Stark- Zeeman Spectroscopy II Details 56:45
Stark- Zeeman Spectroscopy – Anomalous Zeeman effect Details 42:32
Zeeman effect Fine structure, Hyperfine structure II Details

This course is part of NPTEL online courses, delivered by IIT Madras.

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