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arXiv · 1608.04402

Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra

T. Scoquart·J. J. Seaward·S. G. Jackson·M. Olshanii
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Abstract

The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line, related to the symmetry of a regular icosahedron: in two distinct limiting cases the system is constrained to a half-line. We repeat the program for a 600-cell, a four-dimensional generalization of the regular three-dimensional icosahedron.

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T. Scoquart, J. J. Seaward, S. G. Jackson, M. Olshanii. 2016-08-15. Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra. https://doi.org/10.21468/scipostphys.1.1.005

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