PHY 407: QUANTUM MECHANICS II

1. Symmetry in Quantum Mechanics

Symmetry operations and unitary transformations, conservation principles, space and time translations, rotation, space inversion and time reversal, symmetry and degeneracy.

2. Angular Momentum

Rotation operators, angular momentum algebra, eigenvalues of J2 and Jz, spinors and Pauli matrices, addition of angular momenta.

3. Identical Particles

Indistinguishability, symmetric and antisymmetric wave functions, incorporation of spin, Slater determinants, Pauli exclusion principle.

4. Time-independent Approximation Methods

Non-degenerate perturbation theory, degenerate case, Stark effect, Zeeman effect and other examples, variational methods, WKB method, tunnelling.

5. Time-dependent Problems

Schrödinger and Heisenberg picture, time-dependent perturbation theory, transition probability calculations, golden rule, adiabatic approximation, sudden approximation, beta decay as an example.

6. Scattering Theory

Differential cross-section, scattering of a wave packet, integral equation for the scattering amplitude, Born approximation, method of partial waves, low energy scattering and bound states, resonance scattering. Relativistic quantum mechanics: Klein-Gordon and Dirac equations.

References

  1. Leonard I. Schiff, Quantum Mechanics, Fourth Edition, McGraw Hill Education.

  2. Eugen Merzbacher, Quantum Mechanics, Third Edition, Wiley.

  3. L. D. Landau and E.M. Lifshitz, Quantum Mechanics (Non-relatavistic Theory), Third Edition, Butterworth-Heinemann.

  4. Richard P. Feynman, The Feynman Lectures on Physics (Volume 3), The New Millennium Edition, Pearson.

  5. R. Shankar, Principles of Quantum Mechanics, Second Edition, Springer.

  6. J. J. Sakurai, Modern Quantum Mechanics, Second Edition, Pearson.

  7. Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe, Quantum Mechanics (Volume One and Two), Wiley.

  8. Steven Weinberg, Lectures on Quantum Mechanics, Second Edition, Cambridge University Press.

  9. A. Messiah, Quantum Mechanics (Volume One and Two), Dover Publications Inc.

  10. K. Gottfried, Quantum Mechanics, Second Edition, Springer.

Examinations