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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
DOI:
https://doi.org/10.4213/tmf8880
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English version:
Theoretical and Mathematical Physics, 2015, 184:1, 940–952
Bibliographic databases:
Received: 26.01.2015 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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http://mi.mathnet.ru/eng/tmf8880https://doi.org/10.4213/tmf8880 http://mi.mathnet.ru/eng/tmf/v184/i1/p57
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