On the eigenstates of the elliptic Calogero-Moser model

Details On the eigenstates of the elliptic Calogero-Moser model On the eigenstates of the elliptic Calogero-Moser model

2000-02-14

arxiv.org/abs/math/0002104v1

Lett. Math. Phys. 53 (2000) 181-194

Mathematics

Quantum Algebra

10 pages

Scientific paper

It is known that the trigonometric Calogero-Sutherland model is obtained by the trigonometric limit (\tau \to \sqrt{-1} \infty) of the elliptic Calogero-Moser model, where (1,\tau) 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 (2\pi \sqrt{-1} \tau ) 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 (2\pi \sqrt{-1} \tau). With some assumptions, we show analogous results for N-particle and l is positive integer cases.

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