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 Schrödinger-like equation, and we obtain the family of potentials for which this mapping corresponds to a Schrödinger equation with non-minimal coupling.

中文翻译：

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广义动量算子的相对论上下文中的莫尔斯势：肖特基异常，Pekeris 近似和映射

在这项工作中，我们探索了 Dirac 和 Klein-Gordon (KG) 振荡器的泛化，提供了受非广延统计启发的变形线性动量，通过第一原理在相对论环境中提供了莫尔斯势。在 (1 + 1) 维的情况下，相对论振荡器映射到量子莫尔斯势。使用 Pekeris 近似，在 (3 + 1) 维的情况下，我们研究了小号-波状态（l= 0) 的 H ₂、 LiH、 HCl 和 CO 分子（在非相对论极限）和相对论电子，其中肖特基异常（由于莫尔斯光谱的有限性）和自旋对热容量的贡献被报道. 通过重新审视广义的 Pekeris 近似，我们提供了从具有球形势的 (3 + 1) 维 Dirac 和 KG 方程到相关的一维薛定谔方程的映射，并且我们获得了该映射对应的势族到具有非最小耦合的薛定谔方程。