# THE QUANTUM H4 INTEGRABLE SYSTEM

@article{Garcia2010THEQH,
title={THE QUANTUM H4 INTEGRABLE SYSTEM},
author={Marcos A. G. Garc'ia and Alexander V. Turbiner},
journal={Modern Physics Letters A},
year={2010},
volume={26},
pages={433-447}
}
• Published 5 July 2010
• Mathematics
• Modern Physics Letters A
The quantum H4 integrable system is a 4D system with rational potential related to the non-crystallographic root system H4 with 600-cell symmetry. It is shown that the gauge-rotated H4 Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group H4, is in algebraic form: it has polynomial coefficients in front of the derivatives. Any eigenfunction is a polynomial multiplied by ground-state function (factorization property). Spectra correspond to one…
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