Additional analytically exact solutions for three-anyons

Details Additional analytically exact solutions for three-anyons Additional analytically exact solutions for three-anyons

1995-12-08

arxiv.org/abs/hep-th/9512051v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages (RevTex) including 1 postcript figure

Scientific paper

We present new family of exact analytic solutions for three anyons in a harmonic potential (or in free space) in terms of generalized harmonics on $S^3$, which supplement the known solutions. The new solutions satisfy the hard-core condition when $\alpha={1\over 3},1$ ($\alpha$ being the statistical parameter) but otherwise, have finite non-vanishing two-particle colliding probability density, which is consistent with self-adjointness of the Hamiltonian. These solutions, however, do not have one-to-one mapping property between bosonic and fermionic spectra.

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