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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: 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

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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

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