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TMF, 1982, Volume 50, Number 3, Pages 402–409 (Mi tmf2335)  

This article is cited in 3 scientific papers (total in 3 papers)

Goryachev–Chaplygin top in quantum mechanics

I. V. Komarov


Abstract: The quantum analog of the Goryachev–Chaplygin top on the basis of the Euclidean group $E(3)$ is constructed. A representation of the generators of $E(3)$ by functions of two bosch creation and annihilation operators is considered, the problem taking on its most natural form in terms of these operators. For example, the finding of the spectrum of integrals in the Fock representation reduces to finding the eigenvalues of semi-infinite tridiagonal Jacobi matrices; the equations of motion acquire a particularly simple form.

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English version:
Theoretical and Mathematical Physics, 1982, 50:3, 265–270

Bibliographic databases:

Received: 06.01.1981

Citation: I. V. Komarov, “Goryachev–Chaplygin top in quantum mechanics”, TMF, 50:3 (1982), 402–409; Theoret. and Math. Phys., 50:3 (1982), 265–270

Citation in format AMSBIB
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\by I.~V.~Komarov
\paper Goryachev--Chaplygin top in quantum mechanics
\jour TMF
\yr 1982
\vol 50
\issue 3
\pages 402--409
\mathnet{http://mi.mathnet.ru/tmf2335}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=662217}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 50
\issue 3
\pages 265--270
\crossref{https://doi.org/10.1007/BF01016456}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982PK24500010}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. V. Komarov, “Quantum-mechanical Goryachev–Chaplygin top in a strong field”, Theoret. and Math. Phys., 53:2 (1982), 1136–1141  mathnet  crossref  mathscinet  isi
    2. Wolf, T, “Classification of integrable quadratic Hamiltonians on e(3)”, Regular & Chaotic Dynamics, 8:2 (2003), 155  crossref  isi
    3. V. E. Adler, V. G. Marikhin, A. B. Shabat, “Quantum tops as examples of commuting differential operators”, Theoret. and Math. Phys., 172:3 (2012), 1187–1205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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