Eur. Phys. J. Plus (2020) 135: 943
https://doi.org/10.1140/epjp/s13360-020-00951-2

Regular Article

Phase-retrieval from Bohm’s equations

¹ Departamento Acadêmico de Ciências da Natureza (DACIN), Campus Cornélio Procópio (CP), Federal University of Technology – Parana (UTFPR), Avenida Alberto Carazzai 1640, 86300-000, Cornélio Procópio, PR, Brazil
² São Carlos Institute of Physics (IFSC), University of São Paulo (USP), PO Box 369, 13560-970, São Carlos, SP, Brazil

^a carlosbrasil.physics@gmail.com

Received: 17 December 2019
Accepted: 18 November 2020
Published online: 1 December 2020

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 ${\left|\psi (\overrightarrow{r},t)\right|}^2$ and the energy potential $V(\overrightarrow{r},t)$ of a system, how can one determine the complex state $\psi (\overrightarrow{r},t)$? We illustrate our method with three classic examples involving Gaussian states, suggesting applications to quantum state and Hamiltonian engineering.