Abstract:
The completely integrable problem of Kowalewski's top in classical mechanics is
extended to the groups O(4) and O(3,1). For each classical system on the groups O(4), E(3), O(3,1) three inequivalent quantum analogs are found. For the Coulomb problem, this results in the construction of one Kowalewski basis in classical mechanics and three in quantum mechanics.
\Bibitem{Kom81}
\by I.~V.~Komarov
\paper Kowalewski basis for the hydrogen atom
\jour TMF
\yr 1981
\vol 47
\issue 1
\pages 67--72
\mathnet{http://mi.mathnet.ru/tmf2369}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=616440}
\transl
\jour Theoret. and Math. Phys.
\yr 1981
\vol 47
\issue 1
\pages 320--324
\crossref{https://doi.org/10.1007/BF01017022}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981MS49200005}
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Vladimir Dragović, Katarina Kukić, “Systems of Kowalevski Type and Discriminantly Separable Polynomials”, Regul. Chaotic Dyn., 19:2 (2014), 162–184
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