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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
- Published as SciPost Phys. 1, 005 (2016)
|As Contributors:||Maxim Olshanii|
|Submitted by:||Olshanii, Maxim|
|Submitted to:||SciPost Physics|
|Subject area:||Quantum Physics|
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.
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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