An exactly solvable model of the Calogero type for the icosahedral group

TL;DR

This paper introduces an exactly solvable quantum Calogero-type model based on the icosahedral group, providing explicit spectrum calculations and advancing understanding of symmetry-based quantum systems.

Contribution

It constructs and proves the exact solvability of a new Calogero-type model with icosahedral symmetry, a novel application of group theory in quantum mechanics.

Findings

Model is exactly solvable with explicit spectrum

Extends Calogero models to icosahedral symmetry

Provides analytical tools for symmetry-based quantum systems

Abstract

We construct a quantum mechanical model of the Calogero type for the icosahedral group as the structural group. Exact solvability is proved and the spectrum is derived explicitly.