  We consider the non-overlapping wave function paradox of Aharanov \textit{et
al.}, wherein the relative phase between two wave functions cannot be measured
by the moments of position or momentum. We show that there is an unlimited
number of other expectation values that depend on the phase. We further show
that the Wigner distribution is M-indeterminate, that is, a distribution whose
moments do not uniquely determine the distribution. We generalize to more than
two non-overlapping functions. We consider arbitrary representations and show
there is an unlimited number of M-indeterminate distributions. The dual case of
non-overlapping momentum functions is also considered.
