Theoretical and Mathematical Physics

, Volume 184, Issue 1, pp 940–952 | Cite as

Algebraic quantum Hamiltonians on the plane



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.


differential operator with polynomial coefficients classification polynomial form of Calogero–Moser operators 


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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRASMoscowRussia

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