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
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