The Calogero-Sutherland Model and Polynomials with Prescribed Symmetry

Abstract

The Schrödinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have a prescribed symmetry (i.e. be symmetric or antisymmetric) with respect to the interchange of some specified variables. For four particular Calogero-Sutherland systems we construct an eigenoperator for these polynomials which separates the eigenvalues and establishes orthogonality. In two of the cases this involves identifying new operators which commute with the corresponding Schrödinger operators. In each case we express a particular class of the polynomials with prescribed symmetry in a factored form involving the corresponding symmetric polynomials.

LaTeX 2.09, 31 pages

References in corpus (7)

• Exchange Operator Formalism for Integrable Systems of Particles
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• Exact Solution of Long-Range Interacting Spin Chains with Boundaries
• Multicomponent Calogero Model of $B_N$-Type Confined in Harmonic Potential
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