Inverse Time-Dependent Quantum Mechanics

TL;DR

This paper introduces a Bayesian approach to reconstruct quantum potentials from coordinate measurements in non-stationary states, integrating measurement models and prior information within a probabilistic framework.

Contribution

It presents a novel Bayesian method for inverse quantum problems that combines likelihood models with stochastic priors to reconstruct potentials from experimental data.

Findings

Successfully reconstructs quantum potentials from coordinate measurements

Integrates measurement likelihood with prior information in a unified framework

Advances inverse quantum problem-solving techniques

Abstract

Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model, providing the probabilistic description of the measurement process as given by the axioms of quantum mechanics, and 2. additional "a priori" information implemented in form of stochastic processes over potentials.