Quantum action-angle-variable analysis of basic systems

Quantum action-angle variables are used to describe and analyze a number of familiar systems. For a given system, the quantum canonical transformation from the old coordinates, e.g., linear or polar, to the new coordinates, action-angle variables, is found by generalizing the corresponding classical transformation using a method based upon the correspondence principle, the Hermiticity and canonical nature of the old coordinates, and the requirement that the Hamiltonian be independent of the quantum angle variable. The bound-state energy levels and other important system properties follow immediately from the canonical transformation. Harmonic oscillators of various dimensions and the three-dimensional angular momentum system are used as illustrations; these illustrations provide interesting alternatives to the usual quantum treatments.