Abstract
It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (τ→√−1∞) 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√−1τ) 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√−1τ). With some assumptions, we show analogous results for N-particle and l is positive integer cases.
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Takemura, K. On the Eigenstates of the Elliptic Calogero–Moser Model. Letters in Mathematical Physics 53, 181–194 (2000). https://doi.org/10.1023/A:1011073115698
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DOI: https://doi.org/10.1023/A:1011073115698