Bound States of the Dirac Equation for a Class of Effective Quadratic Plus Inversely Quadratic Potentials

TL;DR

This paper provides exact solutions to the Dirac equation with a specific class of potentials, revealing unique bound state properties in two dimensions that differ from non-relativistic cases.

Contribution

It introduces exact solutions for the Dirac equation with quadratic plus inversely quadratic potentials, including the generalized Dirac oscillator as a special case.

Findings

Exact bound state solutions for the Dirac equation with specified potentials.

Demonstrates differences from Schrödinger equation in potential effects.

Links to generalized Dirac oscillator solutions.

Abstract

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schroedinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.