Semi-infinite quantum wells in a position-dependent mass background

TL;DR

This paper derives semi-infinite quantum well models with position-dependent mass profiles using point canonical transformations from known solvable potentials, expanding the class of exactly solvable quantum systems.

Contribution

It introduces new semi-infinite quantum well models with position-dependent mass derived from Morse and Rosen-Morse II potentials, providing exact solutions.

Findings

Models exhibit non-rectangular, semi-infinite profiles

Exact solutions obtained for both Morse and Rosen-Morse II based wells

Mass profiles become infinite at negative positions and constant at large positive positions

Abstract

By using a point canonical transformation starting from the constant-mass Schr\"odinger 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.