Rationally-extended radial harmonic oscillator in a position-dependent mass background

• URL: http://arxiv.org/abs/2512.16510v1
• Date: Thu, 18 Dec 2025 13:23:25 GMT
• Title: Rationally-extended radial harmonic oscillator in a position-dependent mass background
• Authors: Christiane Quesne,
• Abstract summary: We show that the radial harmonic oscillator problem in the position-dependent mass background of the type $m(;r) = (1+r2)-2$, $>0$, can be solved by using a point canonical transformation mapping the corresponding Schrdinger equation onto that of the Pschl-Teller I potential with constant mass.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that the radial harmonic oscillator problem in the position-dependent mass background of the type $m(α;r) = (1+αr^2)^{-2}$, $α>0$, can be solved by using a point canonical transformation mapping the corresponding Schrödinger equation onto that of the Pöschl-Teller I potential with constant mass. The radial harmonic oscillator problem with position-dependent mass is shown to exhibit a deformed shape invariance property in a deformed supersymmetric framework. The inverse point canonical transformation then provides some exactly-solvable rational extensions of the radial harmonic oscillator with position-dependent mass associated with $X_m$-Jacobi exceptional orthogonal polynomials of type I, II, or III. The extended potentials of type I and II are proved to display deformed shape invariance. The spectrum and wavefunctions of the radial harmonic oscillator potential and its extensions are shown to go over to well-known results when the deforming parameter $α$ goes to zero.

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