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

Abstract

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.

12pages, REVTeX

References in corpus (4)

• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• Orthogonal Symmetric Polynomials Associated with the Calogero Model
• The Yangian Symmetry in the Spin Calogero Model and its Applications
• Mapping of the $B_N$-type Calogero-Sutherland-Moser system to decoupled Harmonic Oscillators

Cited by in corpus (9)

• A_N-type Dunkl operators and new spin Calogero-Sutherland models
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• Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
• Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems
• Truncated Calogero-Sutherland models
• Exact ground states of quantum many-body systems under confinement
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
• Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial