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

Scoquart, Thibault; Seaward, Joseph J.; Jackson, Steven Glenn; Olshanii, Maxim

doi:10.21468/SciPostPhys.1.1.005

SciPost Physics

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
pdf
Submissions/Reports

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.1.1.005
TI  - Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra
PY  - 2016/10/23
UR  - https://scipost.org/SciPostPhys.1.1.005
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 1
IS  - 1
SP  - 005
A1  - Scoquart, Thibault
AU  - Seaward, Joseph J.
AU  - Jackson, Steven Glenn
AU  - Olshanii, Maxim
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.1.1.005,
	title={{Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra}},
	author={T. Scoquart and J. J. Seaward and S. G. Jackson and M. Olshanii},
	journal={SciPost Phys.},
	volume={1},
	pages={005},
	year={2016},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.1.1.005},
	url={https://scipost.org/10.21468/SciPostPhys.1.1.005},
}

Cited by 7

Ontology / Topics

See full Ontology or Topics database.

Exactly solvable models Icosahedra Reflection groups

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.

¹ ² Thibault Scoquart,
¹ Joseph J. Seaward,
¹ Steven Glenn Jackson,
¹ Maxim Olshanii

Funders for the research work leading to this publication