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.

## Assessment

Best 2 of 3 quizzes | 20x2 | 40% |
---|---|---|

Final | 60x1 | 60% |

Total | 100% |

## Assignments

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.

### References

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