Morse potential and its relationship with the Coulomb in a position-dependent mass background

Abstract

We provide some explicit examples wherein the Schrödinger equation for the Morse potential remains exactly solvable in a position-dependent mass background. Furthermore, we show how in such a context, the map from the full line $(-\infty ,\infty )$ to the half line $(0,\infty )$ may convert an exactly solvable Morse potential into an exactly solvable Coulomb one. This generalizes a well-known property of constant-mass problems.

9 pages, no figure; final published version

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