## SciPost Submission Page

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

### by T. Scoquart, J. J. Seaward, S. G. Jackson, M. Olshanii

#### - Published as SciPost Phys. 1, 005 (2016)

### Submission summary

As Contributors: | Maxim Olshanii |

Arxiv Link: | https://arxiv.org/abs/1608.04402v4 |

Date accepted: | 2016-10-21 |

Date submitted: | 2016-10-20 |

Submitted by: | Olshanii, Maxim |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approach: | Theoretical |

### 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.

### Ontology / Topics

See full Ontology or Topics database.Published as SciPost Phys. 1, 005 (2016)

### List of changes

1.) Paragraph added to introduction and conclusion about the difficulty extending these solutions to finite delta-interaction potentials.

2.) Clarified labeling convention on the formula governing the mass ratios.

3.) Formula in section 2 was formerly true only for when \mu=M.

4.) Correction of reference pointer on page three and minor spelling corrections