Stability estimate for the relativistic Schr\"odinger equation with time-dependent vector potentials

TL;DR

This paper derives a logarithmic stability estimate for recovering time-dependent vector and scalar potentials in the relativistic Schrödinger equation on a bounded domain, using a geometric optics approach.

Contribution

It introduces a novel stability estimate for inverse problems involving the relativistic Schrödinger equation with time-dependent potentials.

Findings

Logarithmic stability estimate established

Recovery of potentials is stable under certain conditions

Method applicable to bounded cylindrical domains

Abstract

We consider the relativistic Schr\"odinger equation with a time dependent vector and scalar potential on a bounded cylindrical domain. Using a Geometric Optics Ansatz we establish a logarithmic stability estimate for the recovery of the vector and scalar potentials.