PH5170 Quantum Mechanics II

This is the homepage for the second course in quantum mechanics being offered to M.Sc. (Physics) as well as dual degree students at IIT Madras during Spring 2012.

Objectives: This is the second course of two courses in quantum mechanics. It introduces the students to basic aspects of quantum mechanics.


Best 2 of 3 quizzes 20x2 40%
Final 60x1 60%
Total 100%


There will be several ungraded assignments that will be handed out to the student.

Notes and Handouts

An introduction to Special Relativity; The Hubbard Model: Some Rigorous Results and Open Problems by E. Lieb;

Official Course Content

Orbital and spin angular momentum. Angular momentum algebra. Eigenstates and eigenvalues of angular momentum. Addition of angular momenta, Clebsch-Gordan coefficients. Irreducible tensor operators and the Wigner-Eckart theorem.

Systems of identical particles. Symmetric and antisymmetric wavefunctions. Bosons and Fermions. Pauli's exclusion principle. Second quantization, occupation number representation.

Non-relativistic scattering theory. Scattering amplitude and cross-section. The integral equation for scattering. Born approximation. Partial wave analysis. The optical theorem.

Elements of relativistic quantum mechanics. The Klein-Gordon equation. The Dirac equation. Dirac matrices, spinors. Positive and negative energy solutions, physical interpretation. Nonrelativistic limit of the Dirac equation.


  1. J.J. Sakurai, Modern Quantum Mechanics, Benjamin Cummings (1985).
  2. P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press (1991).
  3. L.D. Landau and E.M. Lifshitz, Quantum Mechanics — Nonrelativistic Theory, 3rd Edition, Pergamon (1981).
  4. P.M. Mathews and K. Venkatesan, A Textbook of Quantum Mechanics, Tata McGraw-Hill (1977).
  5. J. Bjorken and S. Drell, Relativistic Quantum Mechanics, McGraw-Hill (1965).
  6. A. Messiah, Quantum Mechanics, Vols. 1 and 2, North Holland (1961).
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