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

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.

arXiv comment9 pages, 3 figures

References in corpus (3)

• Periodic integrable systems with delta-potentials
• Trigonometric Cherednik algebra at critical level and quantum many-body problems
• Traces of Integrability in Relaxation of One-Dimensional Two-Mass Mixtures

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• Traces of integrability in scattering of one-dimensional dimers on a barrier
• One-Dimensional Quantum Systems - From Few to Many Particles