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Quantum Simulation Open Quantum Systems Decoherence Quantum State Preparation Representation

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

arXiv
Authors: C. Quesne

Year

2015

Paper ID

27067

Status

Preprint

Abstract Read

~2 min

Abstract Words

90

Citations

N/A

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.

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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1509.07348 [2] arXiv https://arxiv.org/abs/1509.07348 [3] Publisher https://arxiv.org/abs/1509.07348

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