Abstract

As early as 1933 Pauli posed the question whether the Schrodinger wave function can be uniquely determined from given probability distributions of position and momentum if the quantum state is known beforehand to be in a pure state. It is now well known that for any wave function of definite parity the Pauli problem is not uniquely solvable. Somewhat later Feenberg [1] proved that for one dimensional problems . in principle, the values of W(x,t) = |ψ(x,t₀)|² and (∂/∂t)W(x,t₀) at any given time t₀ uniquely determine ψ(x,t) itself apart from a trivial global phase fac tor. However, the proof merely shows the possibility of a unique determination of ψ(x,t) but yields no algorithm to reconstruct the wave function from this two distributions.

© 1996 IEEE