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

• URL: http://arxiv.org/abs/2005.01250v2
• Date: Fri, 7 Aug 2020 22:52:22 GMT
• Title: Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping
• Abstract summary: We map the Dirac and Klein-Gordon (KG) oscillators into the quantum Morse potential. We study the thermodynamics of the S-waves states (l=0) of the H2, LiHdinger, and CO molecules. We obtain the family of potentials for which this mapping corresponds to a Schr"odinger equation with non-minimal coupling.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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