Advanced Quantum Mechanics

Paper Code: 
24PHY423
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to – 

  • make students understand the concepts of relativistic formulation and Dirac equations
  • develop an understanding about the basics of scattering theory.
  • enable the students to apply quantum mechanical tools  to various types of applications and research.

 

Course Outcomes: 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment 

Strategies

Course

Code

Course Title

24PHY423

 

 

Advanced Quantum Mechanics

(Theory)

 

 

 

CO129: Elaborate upon non relativistic scattering

CO130: Analyse the relativistic quantum mechanical equations, namely, Klein-Gordon equation and Dirac equation.

CO131: Determine Dirac matrices and symmetry conditions.

CO132: Apply quantum theory of radiation and compare Rayleigh and Thomson scattering.

CO133: Develop an understanding of S-matrix and scattering and their applications.

CO134: Contribute effectively in Course specific interaction.

Approach in teaching:

 

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

 

 

Learning activities for the students:

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: 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, 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. Dirac relativistic equation and its general solution. 

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: 
S-Matrix and scattering

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.

Essential Readings: 

·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). 

 

References: 

· 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). 

 

E-Content:

· https://archive.org/details/advanced-quantum-mechanics-by-j.-j.-sakurai-z-lib.org.

· https://www.ebookselibrary.com/book-detail/higher-education/physics/ADVANCED-QUANTUM-MECHANICS-126.

 

 

 

Academic Year: 
2024-2025
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