dorsal/arxiv
View SchemaRelationship Between the Energy Eigenstates of Calogero-Sutherland Models With Oscillator and Coulomb-like Potentials
| Authors | Pijush K. Ghosh, Avinash Khare |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9808005 |
| URL | https://arxiv.org/abs/solv-int/9808005 |
| DOI | 10.1088/0305-4470/32/11/008 |
| Journal | Journal of Physics A : Math. & Gen. 32 (1999) 2129-2140 |
Abstract
We establish a simple algebraic relationship between the energy eigenstates of the rational Calogero-Sutherland model with harmonic oscillator and Coulomb-like potentials. We show that there is an underlying SU(1,1) algebra in both of these models which plays a crucial role in such an identification. Further, we show that our analysis is in fact valid for any many-particle system in arbitrary dimensions whose potential term (apart from the oscillator or the Coulomb-like potential) is a homogeneous function of coordinates of degree -2. The explicit coordinate transformation which maps the Coulomb-like problem to the oscillator one has also been determined in some specific cases.
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"abstract": "We establish a simple algebraic relationship between the energy eigenstates\nof the rational Calogero-Sutherland model with harmonic oscillator and\nCoulomb-like potentials. We show that there is an underlying SU(1,1) algebra in\nboth of these models which plays a crucial role in such an identification.\nFurther, we show that our analysis is in fact valid for any many-particle\nsystem in arbitrary dimensions whose potential term (apart from the oscillator\nor the Coulomb-like potential) is a homogeneous function of coordinates of\ndegree -2. The explicit coordinate transformation which maps the Coulomb-like\nproblem to the oscillator one has also been determined in some specific cases.",
"arxiv_id": "solv-int/9808005",
"authors": [
"Pijush K. Ghosh",
"Avinash Khare"
],
"categories": [
"solv-int",
"cond-mat",
"hep-th",
"nlin.SI"
],
"doi": "10.1088/0305-4470/32/11/008",
"journal_ref": "Journal of Physics A : Math. \u0026 Gen. 32 (1999) 2129-2140",
"title": "Relationship Between the Energy Eigenstates of Calogero-Sutherland Models With Oscillator and Coulomb-like Potentials",
"url": "https://arxiv.org/abs/solv-int/9808005"
},
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