On the eigenstates of the elliptic Calogero-Moser model

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dc.creatorTakemura, Kouichi
dc.date2000-02-14
dc.date.accessioned2026-07-07T04:33:51Z
dc.date.available2026-07-07T04:33:51Z
dc.descriptionIt is known that the trigonometric Calogero-Sutherland model is obtained by the trigonometric limit (τ\to \sqrt{-1} \infty) of the elliptic Calogero-Moser model, where (1,τ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero-Sutherland model, if \exp (2π\sqrt{-1} τ) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero-Moser model which converge to the ones of the Calogero-Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter \exp (2π\sqrt{-1} τ). With some assumptions, we show analogous results for N-particle and l is positive integer cases.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0002104
dc.identifierhttp://arxiv.org/abs/math/0002104
dc.identifierLett. Math. Phys. 53 (2000) 181-194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58681
dc.subjectQuantum Algebra
dc.subjectSpectral Theory
dc.subject82B23; 81R50
dc.titleOn the eigenstates of the elliptic Calogero-Moser model
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