Rotations in Quantum Mechanics

Active and passive rotations, rotation in physical space and state vector space, effect of Euler rotations on coordinate axes, etc. have been discussed in this chapter. Rotation operators for a wave function (a scalar field) and a spinor and their corresponding generators have been derived. Rotation matrices including Euler rotation matrix, their evaluation and properties have been studied. Clebsch-Gordan series for product of two rotation matrices has been derived. Cartesian and spherical tensor operators and their properties under rotations have been discussed. Tensors in physical operators, their matrix elements, Wigner-Eckart theorem and its proof are presented. Multipole expansion of e.m. radiation field and interaction with atoms and nuclei have been discussed.