• Topics

Concept of Symmetries --- Discrete Symmetries and Groups --- Representations, Irreps and reduction to irreps --- character tables

Application to QM: Degeneracies, Matrix elements --- Molecular vibrations

Continuous Groups --- Generators --- Lie Algebra ---- Group Average, Orthogonality and reduction into irreps.

Application to QM: Rotation and Angular Momentum --- Angular Momentum addition --- Harmonic Oscillators, U(1), SU(2) and SU(3)

Application to QM: Symmetry breaking and lifting of degeneracies

Anti-Unitary Implementations of Symmetry: Time Reversal

• References

• J. P. Elliott and P. G. Dawber, Symmetry in Physics, Vol-1

• H. F. Jones, Groups, Representations and Physics

• L. D. Landau and L. M. Lifshitz, Quantum Mechanics

• J. J. Sakurai, Modern Quantum Mechanics

• Lecture Notes

• Lecture 1

• Lecture 2

• Lecture 3

• Lecture 4

• Lecture 5

• Lecture 6

Lecture 7

Lecture 8 (as taught in 2016)