Geodesic
Quasi-St\"ackel systems and two-dimensional Schr\"odinger equations in an~electromagnetic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 83-92

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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. 
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     author = {V. G. Marikhin},
     title = {Quasi-St\"ackel systems and two-dimensional {Schr\"odinger} equations in an~electromagnetic field},
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V. G. Marikhin. Quasi-St\"ackel systems and two-dimensional Schr\"odinger equations in an~electromagnetic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 83-92. http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a2/