English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Based on recent results on quasi-exactly solvable Schrodinger equations, wereview a new phenomenological potential class lately reported. In the presentpaper we consider the quantum differential equations resulting from positiondependent mass (PDM) particles. We focus on the PDM version of the hyperbolicpotential $V(x) = {a}~\text{sech}^2x + {b}~\text{sech}^4x$, which we addressanalytically with no restrictions on the parameters and the energies. This isthe celebrated Manning potential, a double-well widely known in molecularphysics, until now not investigated for PDM. We also evaluate the PDM versionof the sixth power hyperbolic potential $V(x) ={a}~{\text{sech}^6x}+b~{\text{sech}^4x}$ for which we could find exactexpressions 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 particularinterest for its connection to the new trends in atomtronics. The PDMSchrodinger equations studied in the present paper yield analyticaleigenfunctions in terms of local Heun functions in its confluents forms. In allthe cases PDM particles are more likely tunneling than ordinary ones. Inaddition, a merging of eigenstates has been observed when the mass becomesnonuniform.

Energy eigenfunctions for position-dependent mass particles in a new class of molecular hamiltonians