Abstract
Using a point canonical transformation starting from the constant-mass Schrödinger equation for the Morse potential, it is shown that a semi-infinite quantum well model with a non-rectangular profile associated with a position-dependent mass that becomes infinite for some negative value of the position, while going to a constant for a large positive value of the latter can be easily derived. In addition, another type of semi-infinite quantum well associated with the same position-dependent mass is constructed and solved by starting from the Rosen-Morse II potential instead of the Morse one.
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