Generalized relativistic harmonic oscillator in minimal length quantum mechanics

TL;DR

This paper solves the generalized relativistic harmonic oscillator in minimal length quantum mechanics, analyzing bound states for fermions and antifermions, and includes new isolated solutions extending previous results.

Contribution

It provides a comprehensive solution to the relativistic harmonic oscillator in minimal length quantum mechanics, including all potential signs and isolated solutions.

Findings

Bound-state solutions for fermions and antifermions are obtained.

All previously analyzed cases are recovered as special cases.

An isolated solution from the Sturm-Liouville scheme is identified.

Abstract

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermion and antifermions. Furthermore, we also find an isolated solution from the Sturm-Liouville scheme. All cases already analyzed in the literature, are obtained as particular cases.