preprint · arXiv (Cornell University) · 2010

The quantum $H_4$ integrable system

García, Marcos A. G., Turbiner, Alexander V

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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 $\vec \al\ =\ (1,5,8,12)$.

Cite this paper

APA 7

García, M. A. G., & Turbiner, A. V. (2010). The quantum $H_4$ integrable system. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1011.2127

MLA 9

García, Marcos A. G., and Alexander V Turbiner. “The quantum $H_4$ integrable system.” arXiv (Cornell University), 2010, https://doi.org/10.48550/arxiv.1011.2127.

Chicago

García, Marcos A. G., and Alexander V Turbiner. 2010. “The quantum $H_4$ integrable system.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1011.2127.

Harvard

García, M.A.G. and Turbiner, A.V. (2010) ‘The quantum $H_4$ integrable system’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1011.2127.

BibTeX

@misc{garcia2010quantum,
  title = {{The quantum $H_4$ integrable system}},
  author = {García, Marcos A. G. and Turbiner, Alexander V},
  journal = {arXiv (Cornell University)},
  year = {2010},
  doi = {10.48550/arxiv.1011.2127}
}

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