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arXiv · 1503.05185

Algebraic quantum Hamiltonians on the plane

Vladimir Sokolov
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Abstract

We consider second order differential operators $P$ with polynomial coefficients that preserve the vector space $V_k$ of polynomials of degrees not greater then $k$. We assume that the metric associated with the symbol of $P$ is flat and that the operator $P$ is potential. In the case of two independent variables we obtain some classification results and find polynomial forms for the elliptic $A_2$ and $G_2$ Calogero-Moser Hamiltonians and for the elliptic Inosemtsev model.

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Vladimir Sokolov. 2015-03-17. Algebraic quantum Hamiltonians on the plane. https://doi.org/10.1007/s11232-015-0307-x

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