Eigenfunctions for SU(N) particles with 1/r^2 interaction in harmonic confinement

K. Vacek; A. Okiji; N. Kawakami

doi:10.1088/0305-4470/27/7/002

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arXiv · cond-mat/9402012

Eigenfunctions for SU(N) particles with 1/r^2 interaction in harmonic confinement

K. Vacek·A. Okiji·N. Kawakami

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Abstract

We find a set of the exact eigenfunctions which provide the energy spectrum for the quantum $N$-body Calogero-Sutherland model for fermions or bosons with SU($ν$) spin degrees of freedom moving in a harmonic confinement potential. The eigenfunctions are explicitly constructed as a simple product of the Jastrow wave function for the ground state and the Hermite polynomials introduced to generate the excited states. The corresponding energy spectrum is given by a sum of the correlated ground-state energy and of the excited-state energy for SU($ν$) free particles in a harmonic well.

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K. Vacek, A. Okiji, N. Kawakami. 1994-02-03. Eigenfunctions for SU(N) particles with 1/r^2 interaction in harmonic confinement. https://doi.org/10.1088/0305-4470/27/7/002

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