Quantum Mechanics II


(Image Credit: Richard Kail/Getty Images)

Course Summary

This is the second course on Quantum Mechanics intended for IIIed Semester MSc Physics Students at Calicut University. The course is a continuation of Quantum Mechanics I of the second semester  MSc Physics is hence an essential prerequisite for this course. 


The entire course can be broadly classified into three parts. The first part discusses various approximation schemes useful to solve the Schrodinger equations in different situations. In the second part, we will briefly discuss some aspects of Relativistic Quantum Mechanics and the third part of the course will briefly introduce the concepts of "Quantum Field Theory".

Topics covered

A Brief Summary of the Cause is given below. 

  1. Approximation Methods 
    o Time Independent Problems
    o Variation Methods
    o Time-Dependent Perturbation Theory
  2. Relativistic Quantum Mechanics
    o Dirac Equations
    o Solutions of Dirac Equations
    o Hole Theory
    o The Klein-Gordon Equation
  3. Quantum Field Theory 
    o Principles of Canonical Quantization of Fields
    o Lagrangian and Hamiltonian Density
    o Second Quantization of Shrodinger Wave Field For Bosons and Fermions
Complete Syllabus

1. Perturbation Theory: 

The WKB approximation, Connection formulae, Barrier tunneling, Application to decay- bound states, Penetration of a potential barrier, Time- independent perturbation theory, Non-degenerate and generate cases, Anharmonic oscillator, Stark and Zeeman effects in hydrogen. 

2. Variational method: 

The variational equation, ground state, and excited states, the variation method for bound states, Application to the ground state of the hydrogen and helium atoms. 

3. Time-dependent perturbation theory: 

Transition probability, Harmonic perturbation, Interaction of an atom with the electromagnetic field, Induced emission and absorption, The dipole approximation, The Born approximation, and scattering amplitude. 

4. Relativistic Quantum Mechanics:

The Dirac equation, Dirac matrices, Solution of the free-particle Dirac equation, Equation of continuity, Spin of the electron, Non-realistic limit, Spin-orbit coupling, Covariance of the Dirac equation, Bilinear covariants, Hole theory, The Weyl equation, equation for the neutrino, Nonconservation of parity, The Klein Gordon equation, Charge and current densities, The Klein- Gordon equation, Charge and current densities, The Klein -Gordon equation, equation with potentials, Wave equation for the photon, Charge conjugation for the Dirac, Weyl, and Klein Gordon equation. 

5. Quantization of fields: 

The principles of canonical quantization of fields, Lagrangian density and Hamiltonian density, Second quantization of the Schrodinger wave-field for bosons and fermions, Classical field theory of electrodynamics, and gauge symmetry.

6. Quantum Interpretation : 

Quantum measurement- Entanglement- EPR paradox, Hidden variables, Bell's theorem-Experimental test of Bell's Inequality.