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Special Topics in the Theory of Atomic Collisions and Spectroscopy

Special Topics in the Theory of Atomic Collisions and Spectroscopy. 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.
(from nptel.ac.in)

Introduction


Module 0: Introductory Lecture
Lecture 01 - Introduction to the STiTACS Course
Module 1: Quantum Collisions
Lecture 02 - Quantum Theory of Collisions
Lecture 03 - Quantum Theory of Collisions: Optical Theorem
Lecture 04 - Quantum Theory of Collisions: Optical Theorem
Lecture 05 - Quantum Theory of Collisions: Differential Scattering Cross Section
Lecture 06 - Quantum Theory of Collisions: Differential Scattering Cross Section, Partial Wave Analysis
Lecture 07 - Quantum Theory of Collisions: Optical Theorem - Unitarity of the Scattering Operator
Lecture 08 - Quantum Theory of Collisions: Reciprocity Theorem, Phase Shift Analysis
Lecture 09 - Quantum Theory of Collisions: More on Phase Shift Analysis
Lecture 10 - Quantum Theory of Collisions: Resonant Condition in the 1th Partial Wave
Lecture 11 - Quantum Theory of Collisions: Levinson's Theorem
Lecture 12 - Quantum Theory of Collisions: Levinson's Theorem
Module 2: Second Quantization
Lecture 13 - Many Body Theory, Electron Correlations
Lecture 14 - Second Quantization Creation, Destruction and Number Operators
Lecture 15 - Many-particle Hamiltonian and Schrodinger Equation in 2nd Quantization Formalism
Module 3: Electron Gas in the Hartree-Fock and the Random Phase Approximation
Lecture 16 - Many-electron Problem in Quantum Mechanics
Lecture 17 - Hartree-Fock Self-Consistent-Field
Lecture 18 - Exchange, Statistical, Fermi-Dirac Correlations
Lecture 19 - Limitations of the Hartree-Fock Self-Consistent-Field Formalism
Lecture 20 - Many-Body Formalism, Second Quantization
Lecture 21 - Density Fluctuations in an Electron Gas
Lecture 22 - Bohm-Pines Approach to Random Phase Approximation
Lecture 23 - Bohm-Pines Approach to Random Phase Approximation
Lecture 24 - Bohm-Pines Approach to Random Phase Approximation
Module 4: Feynman Diagrammatic Methods
Lecture 25 - Schrodinger, Heisenberg and Dirac Pictures of QM
Lecture 26 - Dyson's Chronological Operator
Lecture 27 - Gell-Mann-Low Theorem
Lecture 28 - Rayleigh-Schrodinger Perturbation Methods and Adiabatic Switching
Lecture 29 - Feynman Diagrams
Lecture 30 - First Order Feynman Diagrams
Lecture 31 - Some More on First Order Feynman Diagrams
Lecture 32 - Second and Higher Order Feynman Diagrams
Module 5: More on Quantum Collisions
Lecture 33 - Lippman Schwinger Equation of Potential Scattering
Lecture 34 - Born Approximation
Lecture 35 - Coulomb Scattering
Module 6: Resonances in Quantum Scattering
Lecture 36 - Scattering of Partial Waves
Lecture 37 - Scattering at High Energy
Lecture 38 - Resonances in Quantum Collisions
Lecture 39 - Breit-Wigner Resonances
Module 7: Fano Analysis of Resonances
Lecture 40 - Fano Parameterization of Breit-Wigner Formula
Lecture 41 - Discrete State Embedded in the Continuum
Lecture 42 - Resonance Life Times
Lecture 43 - Wigner-Eisenbud Formalism of Time-Delay in Scattering
Module 8: Guest Lectures by Professor S.T. Manson
Lecture 44 - Photoionization and Photoelectron Angular Distributions
Lecture 45 - Ionization and Excitation of Atoms by Fast Charged Particles
Lecture 46 - Photo-absorption by Free and Confined Atoms and Ions: Recent Developments

Related Links
Special Topics in the Theory of Atomic Collisions and Spectroscopy
Instructor: Prof. P.C. Deshmukh, Department of Physics, IIT Madras. Syllabus. 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.