标题： 位置依赖质量粒子在一类新的分子哈密顿量中的能量本征函数 显示英文标题

标题： Energy eigenfunctions for position-dependent mass particles in a new family of molecular hamiltonians

摘要： 基于准精确可解薛定谔方程的最新结果，我们回顾了最近在本期刊上发表的一种新的现象学势类 [参见 J. Phys. A: Math. Theor. 45 (2012) 175302]。在本文中，我们考虑由位置依赖质量（PDM）粒子产生的量子微分方程。我们关注双曲势$V(x) = {a}~{\text{sech}^2x} + {b}~{\text{sech}^4x}$的 PDM 版本，我们对其进行解析研究，不限制参数和能量。这就是著名的 Manning 势，一个在分子物理中广为人知的双势阱，直到现在尚未针对 PDM 进行研究，正如我们将在这里所做的那样。我们还评估了六次幂双曲势$V(x) = {a}~{\text{sech}^6x}+b~{\text{sech}^4x}$的 PDM 版本，在某些特殊条件下我们找到了精确表达式。最后，我们研究了一个三势阱情况$V(x) = {a}~{\text{sech}^6x}+b~{\text{sech}^4x}+c~\text{sech}^2x$，由于其与原子电子学新趋势的联系而特别值得关注。本文研究的 PDM 薛定谔方程以局部 Heun 函数的合并形式给出解析本征函数。在所有情况下，PDM 粒子比普通粒子更可能隧穿。此外，当质量变得不均匀时，观察到了本征态的减少或合并。 显示英文摘要

摘要： Based on recent results on quasi-exactly solvable Schrodinger equations, we review a new phenomenological potential class lately reported in this journal [see J. Phys. A: Math. Theor. 45 (2012) 175302]. In the present paper we consider the quantum differential equations resulting from position dependent mass (PDM) particles. We focus on the PDM version of the hyperbolic potential $V(x) = {a}~{\text{sech}^2x} + {b}~{\text{sech}^4x}$, which we address analytically with no restrictions on the parameters and the energies. This is the celebrated Manning potential, a double-well widely known in molecular physics, until now not investigated for PDM as we will do here. We also evaluate the PDM version of the sixth power hyperbolic potential $V(x) = {a}~{\text{sech}^6x}+b~{\text{sech}^4x}$ for which we could find exact expressions under some special settings. Finally, we address a triple-well case $V(x) = {a}~{\text{sech}^6x}+b~{\text{sech}^4x}+c~\text{sech}^2x$ of particular interest for its connection to the new trends in atomtronics. The PDM Schrodinger equations studied in the present paper yield analytical eigenfunctions in terms of local Heun functions in its confluents forms. In all the cases PDM particles are more likely tunneling than ordinary ones. In addition, a reduction or merging of eigenstates has been observed when the mass becomes nonuniform.