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

B. Bagchi·P. S. Gorain·C. Quesne
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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.

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B. Bagchi, P. S. Gorain, C. Quesne. 2006-12-04. Morse potential and its relationship with the Coulomb in a position-dependent mass background. https://doi.org/10.1142/s0217732306021888

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