Article révisé par les pairs
| Résumé : | 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 D = (d+2)/2.. 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. |
