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

M-indeterminate distributions in quantum mechanics and the non-overlapping wave function paradox