  We derive a general expression for the expectation value of the phase
acquired by a time dependent wave function in a multi component system, as
excursions are made in its coordinate space. We then obtain the mean phase for
the (linear dynamic $E \otimes \epsilon$) Jahn-Teller situation in an
electronically degenerate system. We interpret the phase-change as an
observable measure of the {\it effective} nodal structure of the wave function.
