Sliding inverse problems for radial Dirac and Schr\"odinger equations

TL;DR

This paper introduces and solves new sliding inverse and half-inverse problems for radial Schrödinger and Dirac equations, enabling the recovery of these systems from quantum defect data, including Coulomb-type potentials.

Contribution

It presents novel sliding inverse problems for radial quantum systems, expanding the scope of inverse problem solutions to more complex potentials and multidimensional cases.

Findings

Successfully solved sliding inverse problems for radial Schrödinger and Dirac equations.

Extended methods to systems with Coulomb-type potentials.

Applicable to multidimensional Schrödinger equations.

Abstract

New inverse and half-inverse problems: {\it sliding problems} are introduced. In this way several physically important equations are recovered from the quantum defect. In particular, sliding problems are solved for radial Schr\"odinger equation, radial Dirac system and multidimensional Schr\"odinger equation. Systems with Coulomb-type potentials are considered as well.