Rationally-extended radial harmonic oscillator in a position-dependent mass background
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911325811113984 |
|---|---|
| author | Quesne, Christiane |
| author_facet | Quesne, Christiane |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rationally-extended radial harmonic oscillator in a position-dependent mass background Quesne, Christiane Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics 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. |
| title | Rationally-extended radial harmonic oscillator in a position-dependent mass background |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2512.16510 |