Development of a theory of quantum action-angle variables with examples

A quantum theory corresponding to the classical theory of action-angle variables is developed and applied to the examples of a harmonic oscillator and an infinite potential well. The quantum state of the system which is canonically connected to the original system, of action-angle variables are obtained. Using those quantum states, we show that the quantum behavior and the expectation values of some physical quantities, including the energy eigenvalues of the original system, can be found without prior knowledge of the quantum state of the original system. From the uncertainties of the quantum operators of the action-angle variable system, a, quantum state is interpreted as ail amplitude state of the original quantum system.