| Issue |
EPL
Volume 114, Number 1, April 2016
|
|
|---|---|---|
| Article Number | 10001 | |
| Number of page(s) | 5 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/114/10001 | |
| Published online | 25 April 2016 | |
Novel exactly solvable Schrödinger equations with a position-dependent mass in multidimensional spaces obtained from duality
Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles - Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium
Received: 18 November 2015
Accepted: 11 April 2016
A novel exactly solvable Schrödinger equation with a position-dependent mass (PDM) describing a Coulomb problem in D dimensions is obtained by extending the known duality relating the quantum d-dimensional oscillator and D-dimensional Coulomb problems in Euclidean spaces for 
. As an intermediate step, a mapping between a quantum d-dimensional nonlinear oscillator of Mathews-Lakshmanan type (or oscillator in a space of constant curvature) and a quantum D-dimensional Coulomb-like problem in a space of nonconstant curvature is derived. It is finally reinterpreted in a PDM background.
PACS: 03.65.Ge – Solutions of wave equations: bound states
© EPLA, 2016
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