dorsal/arxiv
View SchemaMore on an exactly solvable position-dependent mass Schroedinger equation in two dimensions: Algebraic approach and extensions to three dimensions
| Authors | C. Quesne |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612094 |
| URL | https://arxiv.org/abs/quant-ph/0612094 |
Abstract
An exactly solvable position-dependent mass Schr\"odinger 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. Finally, the two-dimensional model is extended to two integrable and exactly solvable (but not superintegrable) models in three dimensions, depicting a particle in a semi-infinite parallelepipedal or cylindrical channel, respectively.
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"abstract": "An exactly solvable position-dependent mass Schr\\\"odinger equation in two\ndimensions, depicting a particle moving in a semi-infinite layer, is\nre-examined in the light of recent theories describing superintegrable\ntwo-dimensional systems with integrals of motion that are quadratic functions\nof the momenta. To get the energy spectrum a quadratic algebra approach is used\ntogether with a realization in terms of deformed parafermionic oscillator\noperators. In this process, the importance of supplementing algebraic\nconsiderations with a proper treatment of boundary conditions for selecting\nphysical wavefunctions is stressed. Some new results for matrix elements are\nderived. Finally, the two-dimensional model is extended to two integrable and\nexactly solvable (but not superintegrable) models in three dimensions,\ndepicting a particle in a semi-infinite parallelepipedal or cylindrical\nchannel, respectively.",
"arxiv_id": "quant-ph/0612094",
"authors": [
"C. Quesne"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"title": "More on an exactly solvable position-dependent mass Schroedinger equation in two dimensions: Algebraic approach and extensions to three dimensions",
"url": "https://arxiv.org/abs/quant-ph/0612094"
},
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