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Course Co-ordinated by IIT Madras
Coordinators
 
Prof. P.C. Deshmukh
IIT Madras

 

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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.

Module No:

Lecture
No:

Topic

Module 0
Introductory Lecture

01

Introduction to the STiTACS
course

Module 1:
Quantum Collisions

02

Quantum Theory of collisions

03

Quantum Theory of collisions: optical
Theorem

04

Quantum Theory of collisions: optical
Theorem

05

Quantum Theory of collisions: Differential scattering cross section

06

Quantum Theory of collisions: Differential scattering cross section, Partial wave analysis

07

Quantum Theory of collisions: Optical
Theorem – Unitarity of the Scattering
Operator

08

Quantum Theory of collisions:
Reciprocity Theorem, Phase shift analysis

09

Quantum Theory of collisions: More on
Phase shift analysis

10

Quantum Theory of collisions: resonant condition in the lth partial wave.

11

Quantum Theory of collisions: Levinson's theorem

12

Quantum Theory of collisions: Levinson's theorem

Module 2: Second Quantization

13

Many body theory, electron correlations

14

Second Quantization Creation, Destruction and Number operators

15

Many-particle Hamiltonian & Schrodinger Equation in 2nd Quantization formalism

Module 3: Electron Gas in the Hartree-Fock and the Random Phase Approximation

16

Many-electron problem in quantum mechanics

17

Hartree-Fock Self-Consistent-Field

18

Exchange, Statistical, Fermi-Dirac correlations

19

Limitations of the Hartree-Fock Self-Consistent-Field formalism

20

Many-Body formalism, II Quantization

21

Density fluctuations in an electron gas

22

Bohm-Pines approach to Random Phase Approximation

23

Bohm-Pines approach to Random Phase Approximation

24

Bohm-Pines approach to Random Phase Approximation

Module 4:
Feynman Diagrammatic Methods

25

Schrodinger, Heisenberg and Dirac "pictures" of QM

26

Dyson's chronological operator

27

Gell-Mann-Low Theorem

28

Reyleigh-Schrodinger perturbation methods and adiabatic switching

29

Feynman Diagrams

30

I Order Feynman Diagrams

31

II and higher order Feynman Diagrams.

32

Linear response of electron correlations

Module 5: More on Quantum Collisions

33

Lippman Schwinger equation of potential scattering

34

Born Approximation

35

Coulomb scattering

Module 6:Resonances in Quantum Scattering

36

Scattering of partial waves

37

Scattering at high energy

38

Resonances in Quantum Collisions

39

Breit-Wigner Resonances

Module 7: Fano Analysis of Resonances

40

Fano parameterization of Breit-Wigner formula

41

Discrete state embedded in the continuum

42

Resonance life times

43

Wigner-Eisenbud formalism of time-delay in scattering

Module 8:Guest Lectures by Professor S.T.Manson

44

Photoionization and Photoelectron Angular Distributions

45

Ionization and Excitation of Atoms by Fast Charged Particles

46

Photo-absorption by Free and Confined Atoms and Ions: Recent Developments

At least one graduate level course in 'quantum theory', and one in 'atomic physics' is recommended. The previous NPTEL course 'Special/Select Topics in Atomic Physics' given by Dr. P.C.Deshmukh can be useful. This course is available online at the NPTEL weblinks.


  1. Quantum Collisions Theory by C.J.Joachain (Elsevier, 1979)
  2. Quantum Theory of Many Particle Systems by A.L.Fetter and J.D.Walecka (Dover, 2003)
  3. Many Electron Theory by Stanley Raimes (Elsevier, 1972)
  4. Atomic Collisions and Spectra by U.Fano and A.R.P.Rau (Academic Press, 1986)
  5. Atomic Structure Theory: Lectures on Atomic Physics by Walter R. Johnson (Springer; 2007)

  1. https://www.physics.iitm.ac.in/~labs/amp/
  2. https://www.youtube.com/watch?v=2sP5C7Eh8HY
  3. http://nptel.ac.in/courses/115106057/
  4. http://www3.nd.edu/~johnson/
  5. http://www.phy-astr.gsu.edu/manson/

'Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation (Springer Series on Atomic, Optical, and Plasma Physics)' by Ian P. Grant (Springer, 2007)



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