Phase-retrieval from Bohm's equations

TL;DR

This paper introduces an analytic method based on Bohmian equations to solve the phase-retrieval problem in quantum mechanics, enabling the determination of the complex wavefunction from probability density and potential data.

Contribution

The paper presents a novel analytic approach using Bohmian equations for phase-retrieval, demonstrated through classic Gaussian state examples.

Findings

Successfully retrieves quantum states from probability densities and potentials.

Provides a new tool for quantum state and Hamiltonian engineering.

Illustrates method with classical Gaussian examples.

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