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Additional analytically exact solutions for three-anyons

Chaiho Rim
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Abstract

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 $α={1\over 3},1$ ($α$ 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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Chaiho Rim. 1995-12-08. Additional analytically exact solutions for three-anyons. https://arxiv.org/abs/hep-th/9512051

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