Morse potential and its relationship with the Coulomb in a position-dependent mass background
Abstract
We provide some explicit examples wherein the Schr\"odinger 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 (- ∞, ∞) to the half line (0, ∞) 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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