dorsal/arxiv
View SchemaUnified treatment of the Coulomb and harmonic oscillator potentials in $D$ dimensions
| Authors | G. Lévai, B. Kónya, Z. Papp |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9802012 |
| URL | https://arxiv.org/abs/quant-ph/9802012 |
| DOI | 10.1063/1.532595 |
| Journal | J.Math.Phys. 39 (1998) 5811-5823 |
Abstract
Quantum mechanical models and practical calculations often rely on some exactly solvable models like the Coulomb and the harmonic oscillator potentials. The $D$ dimensional generalized Coulomb potential contains these potentials as limiting cases, thus it establishes a continuous link between the Coulomb and harmonic oscillator potentials in various dimensions. We present results which are necessary for the utilization of this potential as a model and practical reference problem for quantum mechanical calculations. We define a Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate the Green's operator on this basis and also present an SU(1,1) algebra associated with it. We formulate the problem for the one-dimensional case too, and point out that the complications arising due to the singularity of the one-dimensional Coulomb problem can be avoided with the use of the generalized Coulomb potential.
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"abstract": "Quantum mechanical models and practical calculations often rely on some\nexactly solvable models like the Coulomb and the harmonic oscillator\npotentials. The $D$ dimensional generalized Coulomb potential contains these\npotentials as limiting cases, thus it establishes a continuous link between the\nCoulomb and harmonic oscillator potentials in various dimensions. We present\nresults which are necessary for the utilization of this potential as a model\nand practical reference problem for quantum mechanical calculations. We define\na Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate\nthe Green\u0027s operator on this basis and also present an SU(1,1) algebra\nassociated with it. We formulate the problem for the one-dimensional case too,\nand point out that the complications arising due to the singularity of the\none-dimensional Coulomb problem can be avoided with the use of the generalized\nCoulomb potential.",
"arxiv_id": "quant-ph/9802012",
"authors": [
"G. L\u00e9vai",
"B. K\u00f3nya",
"Z. Papp"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.532595",
"journal_ref": "J.Math.Phys. 39 (1998) 5811-5823",
"title": "Unified treatment of the Coulomb and harmonic oscillator potentials in $D$ dimensions",
"url": "https://arxiv.org/abs/quant-ph/9802012"
},
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