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 (KG) oscillators, provided with a deformed linear momentum inspired in nonextensive statistics, that gives place to the Morse potential in relativistic contexts by first principles. In the (1+1)-dimensional case the relativistic oscillators are mapped into the quantum Morse potential. Using the Pekeris approximation, in the (3+1)-dimensional case we study the thermodynamics of the S-waves states (l=0) of the H2, LiH, HCl and CO molecules (in the non-relativistic limit) and of a relativistic electron, where Schottky anomalies (due to the finiteness of the Morse spectrum) and spin contributions to the heat capacity are reported. By revisiting a generalized Pekeris approximation, we provide a mapping from (3+1)-dimensional Dirac and KG equations with a spherical potential to an associated one-dimensional Schr\"odinger-like equation, and we obtain the family of potentials for which this mapping corresponds to a Schr\"odinger equation with non-minimal coupling.
Keywords
Cite
@article{arxiv.2005.01250,
title = {Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping},
author = {Ignacio S. Gomez and Esdras S. Santos and Olavo Abla},
journal= {arXiv preprint arXiv:2005.01250},
year = {2021}
}