Novel exactly solvable Schrödinger equations with a position-dependent mass in multidimensional spaces obtained from duality

Abstract

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.

12 pages, no figure; title, abstract and presentation changed

References in corpus (2)

• Ordering ambiguity revisited via position dependent mass pseudo-momentum operators
• An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates

Cited by in corpus (3)

• On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications
• On the classical and quantum dynamics of a class of nonpolynomial oscillators
• Mapping of Two-Dimensional Schrödinger Equation under the Point Transformation