Geodesic
Algebraic quantum Hamiltonians on the plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 57-70 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider second-order differential operators $P$ with polynomial coefficients that preserve the vector space $V_n$ of polynomials of degrees not greater than $n$. We assume that the metric associated with the symbol of $P$ is flat and that $P$ is a potential operator. 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 Inozemtsev model.
Keywords: differential operator with polynomial coefficients, polynomial form of Calogero–Moser operators.
Mots-clés : classification 
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V. V. Sokolov. Algebraic quantum Hamiltonians on the plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 1, pp. 57-70. http://geodesic.mathdoc.fr/item/TMF_2015_184_1_a2/

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