Dirac operator with linear potential and its perturbations

TL;DR

This paper analyzes the Dirac operator with a linear potential, explicitly determining eigenvalues and eigenfunctions, and constructs perturbations with pre-specified spectra, advancing understanding of such operators in mathematical physics.

Contribution

It provides explicit solutions for Dirac operators with linear potentials and develops a method to construct their perturbations with predetermined spectra.

Findings

Eigenvalues and eigenfunctions explicitly derived

Operators generated on axis and half-axis characterized

Perturbations with given spectra constructed

Abstract

We prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in advance given spectra.