Missing solution in a relativistic Killingbeck potential

TL;DR

This paper investigates the bound-state solutions of fermions in a Killingbeck potential with magnetic and AB flux fields, clarifying previous misconceptions and deriving the correct Dirac equation form under spin and pseudo-spin symmetries.

Contribution

It provides the correct quadratic form of the Dirac equation for this system and addresses inaccuracies in prior literature regarding bound-state solutions.

Findings

Correct quadratic Dirac equation form derived

Identified and corrected previous misconceptions

Analyzed bound-state solutions under spin and pseudo-spin symmetries

Abstract

Missing bound-state solutions for fermions in the background of a Killingbeck radial potential including an external magnetic and Aharonov-Bohm (AB) flux fields are examined. The correct quadratic form of the Dirac equation with vector and scalar couplings under the spin and pseudo-spin symmetries is showed and also we point out a misleading treatment in the literature regarding to bound-state solutions for this problem.