Generalized relativistic harmonic oscillator in minimal length quantum mechanics

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 fermions 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.