On inverse problems in electromagnetic field in classical mechanics at fixed energy

TL;DR

This paper investigates inverse scattering and boundary value problems at fixed energy levels for classical mechanics systems influenced by electromagnetic fields, establishing uniqueness theorems for these inverse problems.

Contribution

It extends inverse problem techniques to multidimensional relativistic and nonrelativistic Newton equations with electromagnetic fields, providing new uniqueness results.

Findings

Proved uniqueness theorems for inverse scattering at fixed energy.

Extended inverse problem methods to electromagnetic fields in classical mechanics.

Applicable to both relativistic and nonrelativistic Newton equations.

Abstract

In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic and nonrelativistic Newton equations in a static external electromagnetic field $(V,B)$, $V\in C^2,$ $B\in C^1$ in classical mechanics. Developing the approach going back to Gerver-Nadirashvili 1983's work on an inverse problem of mechanics, we obtain, in particular, theorems of uniqueness.