  A review is given of phase properties in molecular wave functions, composed
of a number of (and, at least, two) electronic states that become degenerate at
some nearby values of the nuclear configuration. Apart from discussing phases
and interference in classical (non-quantal) systems, including light-waves, the
review looks at the constructability of complex wave functions from observable
quantities ("the phase problem"), at the controversy regarding quantum
mechanical phase-operators, at the modes of observability of phase and at the
role of phases in some non-demolition measurements. Advances in experimental
and (especially) theoretical aspects of Aharonov-Bohm and topological (Berry)
phases are described, including those involving two-electron and relativistic
systems. Several works in the phase control and revivals of molecular
wave-packets are cited as developments and applications of complex-function
theory. Further topics that this review touches on are: coherent states,
semiclassical approximations and the Maslov index. The interrelation between
time and the complex state is noted in the contexts of time delays in
scattering, of time-reversal invariance and of the existence of a molecular
time-arrow.
