The massless Dirac-Weyl equation with deformed extended complex potentials

TL;DR

This paper analytically investigates a (2+1)D Dirac equation with a deformed Lorentz scalar potential, transforming it into a Klein-Gordon-like system, and explores its complex Hamiltonian, real spectrum, eigenvectors, and Lie algebraic structure.

Contribution

It introduces a novel approach to solving the Dirac equation with deformed complex potentials and analyzes its algebraic properties and spectrum.

Findings

Real energy spectrum obtained analytically

Complex Hamiltonian characterized and eigenvectors derived

Lie algebraic structure analyzed

Abstract

Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investi gated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective Hamiltonian system. The complex Hamiltonian and its real energy spectrum and eigenvectors are obtained analytically. Moreover, the Lie algebraic analysis is performed.