Quantum Analogue of Ermakov Systems and the Phase of the Quantum Wave Function

Abstract

Based on the multidimensional Ermakov theory, a general result that relates the Schrodinger equation and the Milne equation in terms of a space invariant is established. Using this result not only the role of phase in the Wigner function approach to quantum mechanics is demonstrated but also a better explanation for the Aharonov–Bohm effect is sought in terms of a fundamental phase and the matter-field-coupling current. The existence of a similar space invariant is also emphasized for the nonlinear Schrodinger equation.