Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping

Abstract

In this work we explore a generalization of the Dirac and Klein-Gordon oscillators, where the linear momentum is replaced by a deformed version inspired in nonextensive statistics, that gives place to the Morse potential in both relativistic contexts by first principles. We employ a canonical transformation that maps the harmonic oscillator with a generalized momentum operator into the Morse potential. We study the 1D and the 3D cases, using the Pekeris approximation in the later case. In the non-relativistic limit we reproduce the S-wave states of the H 2 molecule while in the null deformation limit we recover spinless (KG) and spin-orbit (Dirac) oscillators.