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arXiv · 1011.2127

The quantum $H_4$ integrable system

Marcos A. G. García·Alexander V Turbiner
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Abstract

The quantum $H_4$ integrable system is a 4D system with rational potential related to the non-crystallographic root system $H_4$ with 600-cell symmetry. It is shown that the gauge-rotated $H_4$ Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group $H_4$, is in algebraic form: it has polynomial coefficients in front of derivatives. Any eigenfunctions is a polynomial multiplied by ground-state function (factorization property). Spectra corresponds to one of the anisotropic harmonic oscillator. The Hamiltonian has infinitely-many finite-dimensional invariant subspaces in polynomials, they form the infinite flag with the characteristic vector $\vec \al\ =\ (1,5,8,12)$.

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Marcos A. G. García, Alexander V Turbiner. 2010-11-09. The quantum $H_4$ integrable system. https://doi.org/10.1142/s0217751x10050597

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