Rational extensions of an oscillator-shaped quantum well potential in a position-dependent mass background

• URL: http://arxiv.org/abs/2309.11364v2
• Date: Tue, 5 Dec 2023 15:18:17 GMT
• Title: Rational extensions of an oscillator-shaped quantum well potential in a position-dependent mass background
• Authors: C. Quesne
• Abstract summary: A recently proposed quantum well model associated with a position-dependent mass can be solved by applying a point canonical transformation to the constant-mass Schr"odinger equation for the Scarf I potential. Some more involved position-dependent mass models associated with $X$-Jacobi exceptionals are also considered.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that a recently proposed oscillator-shaped quantum well model associated with a position-dependent mass can be solved by applying a point canonical transformation to the constant-mass Schr\"odinger equation for the Scarf I potential. On using the known rational extension of the latter connected with $X_1$-Jacobi exceptional orthogonal polynomials, we build a rationally-extended position-dependent mass model with the same spectrum as the starting one. Some more involved position-dependent mass models associated with $X_2$-Jacobi exceptional orthogonal polynomials are also considered.

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