2000/02/14 by Kouichi Takemura
Mathematics · #math.QA #math.SP #msc:82B23 #msc:81R50
published as Lett. Math. Phys. 53 (2000) 181-194 · 10 pages
arxiv created 2000/02/14 · arxiv updated 2009/11/30
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√(-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√(-1) τ). With some assumptions, we show analogous results for N-particle and l is positive integer cases.