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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- 1 2 Thibault Scoquart,
- 1 Joseph Seaward,
- 1 Steven Glenn Jackson,
- 1 Maxim Olshanii
- 1 École Normale Supérieure [ENS]
- 2 University of Massachusetts Boston / University of Massachusetts Boston