Overview

Instructor: Prof. P.C. Deshmukh, Department of Physics, IIT Madras.

This course builds on the previous NPTEL course 'Special/Select Topics in Atomic Physics' given by Dr. P.C. Deshmukh and aims at preparing senior students for graduate research in some key areas of theoretical atomic physics. The course is covered in 7 Modules. The focus of this course is set on providing the tools that are necessary to study, and engage in, some frontier research areas of theoretical atomic physics. Methods of quantum collision theory, partial waves phase shift analysis, ingoing and outgoing boundary conditions, time-reversal symmetry etc. are introduced. The student is then taken through the methods of second quantization and approximation methods in addressing many-electron correlations, with a special emphasis on the random phase approximation. Feynman diagrammatic methods are introduced. An introduction to the quantum defect theory is provided and some applications of these techniques are summarized.

Syllabus

Mod-01 Lec-01 Introduction to the STiTACS course.
Mod-01 Lec-02 Quantum Theory of collisions.
Mod-01 Lec-03 Quantum Theory of collisions: Optical Theorem.
Mod-01 Lec-04 Quantum Theory of collisions: optical Theorem.
Mod-01 Lec-05 Quantum Theory of collisions: Differential scattering cross section.
Mod-01 Lec-06 Quantum Theory of collisions Differential scattering cross section,Partial wave.
Mod-01 Lec-7 Quantum Theory of collisions: Optical Theorem -- Unitarity of the Scattering Operator.
Mod-01 Lec-08 Quantum Theory of collisions: Reciprocity Theorem, Phase shift analysis.
Mod-01 Lec-09 Quantum Theory of collisions: More on Phase shift analysis.
Mod-01 Lec 10 Quantum Theory of collisions: resonant condition in the l th partial wave..
Mod-01 Lec -11 Quantum Theory of collisions: Levinson's theorem.
Mod-01 Lec 12 Quantum Theory of collisions: Levinson's theorem..
Mod-02 Lec-13 Many body theory, electron correlations.
Mod-02 Lec-14 Second Quantization Creation, Destruction and Number operators.
Mod-02 Lec-15 Many-particle Hamiltonian & Schrodinger Equation in 2nd Quantization.
Mod-03 Lec-16 Many-electron problem in quantum mechanics.
Mod-03 Lec-17 Hartree-Fock Self-Consistent-Field.
Mod-03 Lec-18 Exchange, Statistical, Fermi-Dirac correlations.
Mod-03 Lec-19 Limitations of the Hartree-Fock Self-Consistent-Field formalism.
Mod-03 Lec-20 Many-Body formalism, II Quantization.
Mod-03 Lec-21 Density fluctuations in an electron gas.
Mod-03 Lec-22 Bohm-Pines approach to Random Phase Approximation.
Mod-03 Lec-23 Bohm-Pines approach to Random Phase Approximation..
Mod-03 Lec-24 Bohm-Pines approach to Random Phase Approximation...
Mod-04 Lec-25 Schrodinger, Heisenberg and Dirac "pictures" of QM.
Mod-04 Lec-26 Dyson's chronological operator.
Mod-04 Lec-27 Gell-Mann-Low Theorem.
Mod-04 Lec-28 Reyleigh-Schrodinger perturbation methods and adiabatic switching.
Mod-04 Lec-29 Feynman Diagrams.
Mod-04 Lec-30 I Order Feynman Diagrams.
Mod-04 Lec-31 Some more I Order Feynman Diagrams.
Mod-04 Lec-32 II and higher order Feynman Diagrams..
Mod-05 Lec-33 Lippman Schwinger equation of potential scattering.
Mod-05 Lec-34 Born Approximation.
Mod-05 Lec-35 Coulomb scattering.
Mod-06 Lec-36 Scattering of partial waves.
Mod-06 Lec-37 Scattering at high energy.
Mod-06 Lec-38 Resonances in Quantum Collisions.
Mod-06 Lec-39 Breit-Wigner Resonances.
Mod-07 Lec-40 Fano parameterization of Breit-Wigner formula.
Mod-07 Lec-41 Discrete state embedded in the continuum.
Mod-07 Lec-42 Resonance life times.
Mod-07 Lec-43 Wigner-Eisenbud formalism of time-delay in scattering.
Mod-08 Lec-44 Photoionization and Photoelectron Angular Distributions.
Mod-08 Lec-45 Ionization and Excitation of Atoms by Fast Charged Particles.
Mod-08 Lec-46 Photo-absorption by Free and Confined Atoms and Ions: Recent Developments.