dorsal/arxiv
View SchemaThe Calogero-Sutherland Model and Polynomials with Prescribed Symmetry
| Authors | T. H. Baker, P. J. Forrester |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9609010 |
| URL | https://arxiv.org/abs/solv-int/9609010 |
| DOI | 10.1016/S0550-3213(97)00112-0 |
Abstract
The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have a prescribed symmetry (i.e. be symmetric or antisymmetric) with respect to the interchange of some specified variables. For four particular Calogero-Sutherland systems we construct an eigenoperator for these polynomials which separates the eigenvalues and establishes orthogonality. In two of the cases this involves identifying new operators which commute with the corresponding Schr\"odinger operators. In each case we express a particular class of the polynomials with prescribed symmetry in a factored form involving the corresponding symmetric polynomials.
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"abstract": "The Schr\\\"odinger operators with exchange terms for certain\nCalogero-Sutherland quantum many body systems have eigenfunctions which factor\ninto the symmetric ground state and a multivariable polynomial. The polynomial\ncan be chosen to have a prescribed symmetry (i.e. be symmetric or\nantisymmetric) with respect to the interchange of some specified variables. For\nfour particular Calogero-Sutherland systems we construct an eigenoperator for\nthese polynomials which separates the eigenvalues and establishes\northogonality. In two of the cases this involves identifying new operators\nwhich commute with the corresponding Schr\\\"odinger operators. In each case we\nexpress a particular class of the polynomials with prescribed symmetry in a\nfactored form involving the corresponding symmetric polynomials.",
"arxiv_id": "solv-int/9609010",
"authors": [
"T. H. Baker",
"P. J. Forrester"
],
"categories": [
"solv-int",
"math.QA",
"nlin.SI",
"q-alg"
],
"doi": "10.1016/S0550-3213(97)00112-0",
"title": "The Calogero-Sutherland Model and Polynomials with Prescribed Symmetry",
"url": "https://arxiv.org/abs/solv-int/9609010"
},
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