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

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 Schrödinger 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.