Phase evolution in a multicomponent system

We derive a general expression for the expectation value of the phase acquired by a time dependent wave function in a multicomponent system, as excursions are made in its coordinate space. We then obtain the mean phase for the (linear dynamic [Formula Presented] Jahn-Teller situation in an electronically degenerate system. We interpret the phase-change as an observable measure of the effective nodal structure of the wave function.