ADVANCED QUANTUM MECHANICS

Paper Code: 
PHY 423
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to –

1.     To make students understand the concepts of relativistic formulation and Dirac equations

2.     To develop an understanding about  the basics of scattering theory.

3.     To enable the students to apply quantum mechanical tools  to various types of applications and research.

Course outcomes (COs):

                     Course

Learning outcome (at course level)

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

PHY 423

Advanced Quantum Mechanics

(Theory)

The students will be able to –

 

CO 135:  Describe the basic Hilbert space structures describing all quantum field theories.

 

CO 136:  explain the relativistic quantum mechanical equations, namely, Klein-Gordon equation and Dirac equation.

 

 

CO 137:  Knowledge of interaction of Bosons and Fermions particles .

 

CO 138:  describe second quantization and related concepts.

 

 

CO 139:  Explain the formalism of relativistic quantum field theory.

 

CO 140:  draw and explain Feynman graphs for different interactions.

 

 

CO 141:  Model physical systems using common approximation techniques for making dynamical calculations.

 

CO 142:  Critically analyse probability current density for a fully defined quantum theory.

 

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, , Demonstration, Problem Solving in tutorials

 

 

 

 

 

 

 

Learning activities for the students:

Self learning assignments, Effective questions,  Seminar presentation, Solving numerical.

Additional learning through online videos and MOOC courses

Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations

 

13.00
Unit I: 
Scattering (non-relativistic)
Differential and total scattering cross section, transformation from CM frame to Lab frame, solution of scattering problem by the method of partial wave analysis, expansion of a plane wave into a spherical wave and scattering amplitude, the optical theorem, Applications: scattering from a delta potential, square well potential and the hard sphere scattering of identical particles, energy dependence and resonance scattering, Breit-Wigner formula, quasi stationary states, Lippman-Schwinger equation and the Green's functions approach for scattering problem, Born approximation and its validity for scattering problem, Coulomb scattering problem under first Born approximation in elastic scattering.
                                                                  
9.00
Unit II: 
Relativistic Formulation and Dirac Equation
Attempt for relativistic formulation of quantum theory, The Klein-Gordon equation, Probability density and probability current density, solution of free particle KG equation in momentum representation, interpretation of negative probability density and negative energy solutions. 
                                                                 
11.00
Unit III: 
Dirac equation and Symmetry considerations
Properties of Dirac matrices and algebra of gamma matrices, non-relativistic correspondence of the Pauli equation (inclusive of electromagnetic interaction), Solution of free particle Dirac equation, orthogonality and completeness, relations for Dirac spinors, interpretation of negative energy solution, Lorentz covariance of Dirac equation, charge conjugation (C), Parity(P), time reversal (T) , CPT theorem, Zitterbewegung.
                                                                  
14.00
Unit IV: 
Quantum Theory of Radiation
Classical radiation field, transversality condition, Fourier decomposition and radiation oscillators, Quantization of radiation oscillator, creation, annihilation and number operators, photon states, photon as a quantum mechanical excitations of the radiation field, fluctuations and the uncertainty relation, validity of the classical description, matrix element for emission and absorption, spontaneous emission in the dipole approximation, Rayleigh scattering. Thomson scattering and the Raman effect, Radiation damping and Resonance fluorescence.
 
                                                                 
13.00
Unit V: 
Scattering and Pair Production
S-matrix, S-matrix expansion, Wick's theorem, Diagrammatic representation in configuration space, the momentum representation, Feynman diagrams of basic processes. Applications of S-matrix formalism: The Coulomb scattering, Bhabha scattering, Compton scattering and Pair production.
 
 
 
 
 

BOOKS RECOMMENDED:

  • Ashok Das and A.C. Milissiones : Quantum mechanics - A Modern Approach (Garden and Breach Science Publishers).
  • E. Merzbaker : Quantum Mechanics, Second Edition (John Wiley and Sons).
  • Bjorken and Drell : Relativistic Quantum Mechanics (McGraw Hill).
  • J.J. Sakurai : Advanced Quantum Mechanics (John Wiley)
  • Quantum Field Theory by F. Mandal & G. Shaw (Honh-Wiley).
  • Element of Advanced Quantum Theory by J.M. Ziman. (Cambridge University Press).

 

References: 
 
 
Academic Year: 
2020-2021
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