• DOI:10.1142/S0217732321501406
• Corpus ID: 221090678

Morse potential in relativistic contexts from generalized momentum operator: Schottky anomalies, Pekeris approximation and mapping

@article{Gomez2020MorsePI,
  title={Morse potential in relativistic contexts from generalized momentum operator: Schottky anomalies, Pekeris approximation and mapping},
  author={Ignacio S. Gomez and Esdras S. Santos and Olavo Abla},
  journal={arXiv: Mathematical Physics},
  year={2020}
}

• I. Gomez, E. S. Santos, O. Abla
• Published 4 May 2020
• Physics
• arXiv: Mathematical Physics

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.