New two-parametric family of exactly solvable Dirac Hamiltonians

TL;DR

This paper introduces a new two-parameter family of exactly solvable Dirac Hamiltonians constructed via Darboux transformations, analyzing their spectral properties and eigenfunctions.

Contribution

It presents a novel two-parametric family of exactly solvable Dirac Hamiltonians and explores their spectral characteristics and eigenfunctions.

Findings

Explicit forms of eigenfunctions derived

Spectral properties of the Hamiltonians analyzed

Intertwining relations established between family members

Abstract

We construct a two-parametric family of exactly solvable Dirac Hamiltonians by the Darboux transformation method. We obtain intertwining relations between different members of the Hamiltonian family. We investigate the spectral properties of the obtained Hamiltonians and the explicit forms of their eigenfunctions.