## 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

SciPost Phys. 1, 005 (2016) · published 23 October 2016

- doi: 10.21468/SciPostPhys.1.1.005
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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.

### Cited by 4

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

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^{1 }^{2 }Thibault Scoquart, -
^{1 }Joseph Seaward, -
^{1 }Steven Glenn Jackson, -
^{1 }Maxim Olshanii

^{1}University of Massachusetts Boston / University of Massachusetts Boston^{2}École Normale Supérieure [ENS]

Funders for the research work leading to this publication