This article is cited in 2 papers

Quasi-Stäckel systems and two-dimensional Schrödinger equations in an electromagnetic field

V. G. Marikhin

Landau Institute of Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia

Abstract: We obtain the complete classification of two-dimensional Schrödinger equations in an electromagnetic field with an additional integral quadratic in momenta. For this, we use a Kovalevskaya-type change of variables and reduce the Hamiltonians to a quasi-Stäckel form. In that form, we perform the classification in the Painlevé sense and then return to the original variables.

Keywords: quantum top, integrability, Schrödinger equation.

Received: 14.04.2013

DOI: 10.4213/tmf8540

 English version: Theoretical and Mathematical Physics, 2013, 177:1, 1352–1360

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