Abstract
We present an analytic method, based on the Bohmian equations for quantum mechanics, for approaching the phase-retrieval problem in the following formulation: By knowing the probability density ψ(r,t) ² and the energy potential V(r,t) of a system, how can one determine the complex state ψ(r,t)? We illustrate our method with three classic examples involving Gaussian states, suggesting applications to quantum state and Hamiltonian engineering.