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 TMF, 2015, Volume 184, Number 1, Pages 57–70 (Mi tmf8880)

Algebraic quantum Hamiltonians on the plane

V. V. Sokolov

Landau Institute for Theoretical Physics, RAS, Moscow, Russia

Abstract: 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, classification, polynomial form of Calogero–Moser operators

 Funding Agency Grant Number Fundação de Amparo à Pesquisa do Estado de São Paulo 2014/00246-2

DOI: https://doi.org/10.4213/tmf8880

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English version:
Theoretical and Mathematical Physics, 2015, 184:1, 940–952

Bibliographic databases:

Revised: 05.03.2015

Citation: V. V. Sokolov, “Algebraic quantum Hamiltonians on the plane”, TMF, 184:1 (2015), 57–70; Theoret. and Math. Phys., 184:1 (2015), 940–952

Citation in format AMSBIB
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\by V.~V.~Sokolov
\paper Algebraic quantum Hamiltonians on the~plane
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\vol 184
\issue 1
\pages 57--70
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\jour Theoret. and Math. Phys.
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