ANGLE AND PHASE COORDINATES IN QUANTUM MECHANICS

A general approach to the description of an angle and phase is given on the basis of the kq representation. It is shown that an angular coordinate in quantum mechanics has to be treated as a quasicoordinate in order to avoid inconsistencies. The kq representation leads to a consistent definition of the angular-momentum-angle degree of freedom. Using the correspondence between classical and quantum mechanics for the phase of a harmonic oscillator, operators are defined that form a new quantum-mechanical representation. This representation clarifies the concept of the phase and sheds light on the general understanding of rotations in quantum mechanics. © 1969 The American Physical Society.