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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

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Maxim Olshanii
Submission information
Preprint Link:  (pdf)
Date accepted: 2016-10-21
Date submitted: 2016-10-20 02:00
Submitted by: Olshanii, Maxim
Submitted to: SciPost Physics
Ontological classification
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.

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

Published as SciPost Phys. 1, 005 (2016)

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