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TMF, 1974, Volume 21, Number 1, Pages 60–73 (Mi tmf3857)  

This article is cited in 6 scientific papers (total in 6 papers)

Finiteness of the discrete spectrum in the quantum $n$-particle problem

G. M. Zhislin


Abstract: Sufficient conditions are found for the finiteness of the discrete spectrum of the energy operators of quantum many-particle systems in spaces of functions of given symmetry. These conditions enable one in many cases to reduce the problem of the finiteness of the discrete spectrum of the energy operator of a many-particle system to the analogous problem for a two-particle system.

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English version:
Theoretical and Mathematical Physics, 1974, 21:1, 971–980

Bibliographic databases:

Received: 31.10.1973

Citation: G. M. Zhislin, “Finiteness of the discrete spectrum in the quantum $n$-particle problem”, TMF, 21:1 (1974), 60–73; Theoret. and Math. Phys., 21:1 (1974), 971–980

Citation in format AMSBIB
\Bibitem{Zhi74}
\by G.~M.~Zhislin
\paper Finiteness of the discrete spectrum in the quantum $n$-particle problem
\jour TMF
\yr 1974
\vol 21
\issue 1
\pages 60--73
\mathnet{http://mi.mathnet.ru/tmf3857}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=464996}
\transl
\jour Theoret. and Math. Phys.
\yr 1974
\vol 21
\issue 1
\pages 971--980
\crossref{https://doi.org/10.1007/BF01035594}


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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. M. A. Antonets, G. M. Zhislin, I. A. Shereshevskii, “On the infiniteness of the discrete spectrum of the energy operator of a system of $n$ particles”, Math. USSR-Sb., 28:1 (1976), 27–39  mathnet  crossref  mathscinet  zmath  isi
    2. S. A. Vugal'ter, G. M. Zhislin, “Finiteness of the discrete spectrum of many-particle Hamiltonians in symmetry spaces”, Theoret. and Math. Phys., 32:1 (1977), 602–614  mathnet  crossref  mathscinet
    3. S. A. Vugal'ter, G. M. Zhislin, “On finiteness of the discrete spectrum of the energy operators of multiatomic molecules”, Theoret. and Math. Phys., 55:1 (1983), 357–365  mathnet  crossref  mathscinet  isi
    4. S. A. Vugal'ter, G. M. Zhislin, “On the discrete spectrum of the energy operator of one- and two-dimensional quantum three-particle systems”, Theoret. and Math. Phys., 55:2 (1983), 493–502  mathnet  crossref  mathscinet  isi
    5. S. A. Albeverio, S. N. Lakaev, Zh. I. Abdullaev, “On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator”, Funct. Anal. Appl., 36:3 (2002), 212–216  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Yu. Kh. Eshkabilov, R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 170:3 (2012), 341–353  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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