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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

Submission summary

As Contributors: Maxim Olshanii
Arxiv Link: (pdf)
Date accepted: 2016-10-21
Date submitted: 2016-10-20 02:00
Submitted by: Olshanii, Maxim
Submitted to: SciPost Physics
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


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

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Exactly solvable models Icosahedra Reflection groups

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

Submission & Refereeing History

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Resubmission 1608.04402v4 on 20 October 2016

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