Energy eigenfunctions for positiondependent mass particles in a new class of molecular Hamiltonians
Abstract
Based on recent results on quasiexactly solvable Schrodinger equations, we review a new phenomenological potential class lately reported. 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 doublewell widely known in molecular physics, until now not investigated for PDM. 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 triplewell 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 merging of eigenstates has been observed when the mass becomes nonuniform.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 September 2014
 DOI:
 10.1063/1.4894056
 arXiv:
 arXiv:1403.0302
 Bibcode:
 2014JMP....55i2102C
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 31 pages, 17 figures, 4 tables. Some references corrected. Accepted for publication in J. Math. Phys