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Open Quantum Systems Decoherence

Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions

arXiv
Authors: Christiane Quesne

Year

2007

Paper ID

50254

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

0

Abstract

An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schrödinger equations.

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  • An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0705.2577 [2] arXiv https://arxiv.org/abs/0705.2577 [3] Publisher https://arxiv.org/abs/0705.2577

Local Citation Graph (Related-Paper Links)

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External citation index: OpenAlex citation signal • updated 2026-06-12 16:08:51

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