New Non-Symmetric Orthogonal Basis for the Calogero Model with Distinguishable Particles

We demonstrate an algebraic construction of all the simultaneous eigenfunctions of the conserved operators for distinguishable particles governed by the Calogero Hamiltonian. Our construction is completely parallel to the construction of the Fock space for decoupled quantum harmonic oscillators. The simultaneous eigenfunction does not coincide with the non-symmetric Hi-Jack polynomial, which shows that the conserved operators derived from the number operators of the decoupled quantum harmonic oscillators are algebraically different from the known ones derived by the Dunkl operator formulation. 03.65.Ge, 03.65.Fd, 02.90.+p Typeset using REVTEX 1 There has been a surge of interest in the orthogonal symmetric polynomials associated with the quantum integrable systems with inverse-square long-range interactions. Particularly after the Jack polynomials, which span the orthogonal basis for the Sutherland model [1–4], enabled an exact calculation of dynamical density-density correlation functions of the model [5], the Jack polynomial and its variants have been extensively studied. So far, we have been studying the Hi-Jack (or multivariable Hermite) symmetric polynomial that forms the symmetric orthogonal basis for the Calogero model [6–10], ĤC = 1 2 N