%0 Journal Article
%T Algebraic quantum Hamiltonians on the plane
%A Vladimir Sokolov
%J Physics
%D 2015
%I arXiv
%R 10.1007/s11232-015-0307-x
%X 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.
%U http://arxiv.org/abs/1503.05185v1