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TMF, 1984, Volume 60, Number 3, Pages 413–422 (Mi tmf5355)  

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

Eigenfunctions of quadratic Hamiltonians in the Wigner representation

È. A. Akhundova, V. V. Dodonov, V. I. Man'ko


Abstract: Exact solutions of the Schrödinger equation in the Wigner representation are obtained for an arbitrary time-dependent $N$-dimensional quadratic Hamiltonian. It is shown that a complete system of solutions can always be chosen in the form of products of $N$ Laguerre polynomials having arguments that are quadratic integrals of the motion of the corresponding classical problem. The generating function found for the transition probabilities between the Foek states is a multidimensional generalization of Husimi's well-known expression for an oscillator with variable frequency. The motion of a charged particle in a uniform time-dependent electromagnetic field is considered in detail as an example.

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English version:
Theoretical and Mathematical Physics, 1984, 60:3, 907–913

Bibliographic databases:

Received: 16.01.1984

Citation: È. A. Akhundova, V. V. Dodonov, V. I. Man'ko, “Eigenfunctions of quadratic Hamiltonians in the Wigner representation”, TMF, 60:3 (1984), 413–422; Theoret. and Math. Phys., 60:3 (1984), 907–913

Citation in format AMSBIB
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\by \`E.~A.~Akhundova, V.~V.~Dodonov, V.~I.~Man'ko
\paper Eigenfunctions of quadratic Hamiltonians in the Wigner representation
\jour TMF
\yr 1984
\vol 60
\issue 3
\pages 413--422
\mathnet{http://mi.mathnet.ru/tmf5355}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=768169}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 60
\issue 3
\pages 907--913
\crossref{https://doi.org/10.1007/BF01017893}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984AEF5000008}


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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. V. S. Popov, “Feynman disentangling оf noncommuting operators and group representation theory”, Phys. Usp., 50:12 (2007), 1217–1238  mathnet  crossref  crossref  adsnasa  isi
    2. V. A. Andreev, D. M. Davidovich, L. D. Davidovich, M. D. Davidovich, V. I. Man'ko, M. A. Man'ko, “A transformational property of the Husimi function and its relation to the Wigner function and symplectic tomograms”, Theoret. and Math. Phys., 166:3 (2011), 356–368  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    3. K. V. Chukbar, “Harmony in a many-particle quantum problem”, Phys. Usp., 61:4 (2018), 389–396  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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