Some properties of the Calogero-Sutherland model with reflections

D. Serban

doi:10.1088/0305-4470/30/12/012

Some properties of the Calogero-Sutherland model with reflections

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Abstract

We prove that the Calogero-Sutherland model with reflections (the BC_N model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wavefunctions for certain particular cases (associated with the root systems of the classical Lie groups B_N, C_N and D_N) is also discussed.

Original language	English
Pages (from-to)	4215-4225
Number of pages	11
Journal	Journal of Physics A: Mathematical and General
Volume	30
Issue number	12
DOIs	https://doi.org/10.1088/0305-4470/30/12/012
Publication status	Published - 21 Jun 1997
Externally published	Yes

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10.1088/0305-4470/30/12/012

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title = "Some properties of the Calogero-Sutherland model with reflections",

abstract = "We prove that the Calogero-Sutherland model with reflections (the BCN model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wavefunctions for certain particular cases (associated with the root systems of the classical Lie groups BN, CN and DN) is also discussed.",

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N2 - We prove that the Calogero-Sutherland model with reflections (the BCN model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wavefunctions for certain particular cases (associated with the root systems of the classical Lie groups BN, CN and DN) is also discussed.

AB - We prove that the Calogero-Sutherland model with reflections (the BCN model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wavefunctions for certain particular cases (associated with the root systems of the classical Lie groups BN, CN and DN) is also discussed.

U2 - 10.1088/0305-4470/30/12/012

DO - 10.1088/0305-4470/30/12/012

M3 - Article

AN - SCOPUS:0031582463

SN - 0305-4470

VL - 30

SP - 4215

EP - 4225

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 12

ER -

Some properties of the Calogero-Sutherland model with reflections

Abstract

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