Abstract
We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Here, we factorize the ground stateout of the Hamiltonian H in order to get the new operatorwhich preserves some spaces of polynomialsin the case of equal masses, i.e. (the usual Calogero model) and in the case with different masses. The spectrum of these both cases is found easily.
Highlights
The ordinary Cologero [1,2] model describes N indistinguishable particles on the line which interact through an inverse-square two-body interaction
We study a multispecies one-dimensional Calogero model with two- and three-body interactions
After performing a certain transformation of the operator H, we get a new Hamiltonian H for which we find its spectrum in the both cases with equal masses and different masses
Summary
The ordinary Cologero [1,2] model describes N indistinguishable particles on the line which interact through an inverse-square two-body interaction. The model is completely integrable in both the classical and quantum case [3]. The spectrum is known and the wave functions are given implicitly. In the present paper, which is in a sense a continuation of the investigation of the ordinary model [4], we use an algebraic method to find some of the salient features of the multispecies Calogero model on the line with two- and three-body interactions. After performing a certain transformation of the operator H, we get a new Hamiltonian H for which we find its spectrum in the both cases with equal masses and different masses
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