A Guide to Rotations in Quantum Mechanics

Abstract

To lay a foundation for the study and use of rotation operators in graduate quantum mechanics and in research, a thorough discussion is presented of rotations in Euclidean three space (R3 ) and of their effect on kets in the Hilbert space of a single particle. The Wigner D-matrices are obtained and used to rotate spherical harmonics. An extensive ready-reference appendix of the properties of these matrices, expressed in a consistent notation, is provided. Careful attention is paid throughout to various conventions (e.g. active versus passive viewpoints) that are used in the literature.