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TMF, 1977, Volume 32, Number 1, Pages 70–87 (Mi tmf3137)  

This article is cited in 5 scientific papers (total in 5 papers)

Finiteness of the discrete spectrum of many-particle Hamiltonians in symmetry spaces

S. A. Vugal'ter, G. M. Zhislin


Abstract: Sufficient conditions are found of the finiteness of discrete spectrum of energy operators (in terms of the coordinate and momentum representation) in the symmetry spaces for many-particle systems for which the boundary of continuous spectrum of the Hamiltonian is determined by the dividing into two stable subsystems. In particular, molecules, negative ions of any atoms and systems with short-range interactions are considered. For the systems under consideration the results obtained generalize those known earlier.

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English version:
Theoretical and Mathematical Physics, 1977, 32:1, 602–614

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Received: 21.05.1976

Citation: S. A. Vugal'ter, G. M. Zhislin, “Finiteness of the discrete spectrum of many-particle Hamiltonians in symmetry spaces”, TMF, 32:1 (1977), 70–87; Theoret. and Math. Phys., 32:1 (1977), 602–614

Citation in format AMSBIB
\Bibitem{VugZhi77}
\by S.~A.~Vugal'ter, G.~M.~Zhislin
\paper Finiteness of the discrete spectrum of many-particle Hamiltonians in symmetry spaces
\jour TMF
\yr 1977
\vol 32
\issue 1
\pages 70--87
\mathnet{http://mi.mathnet.ru/tmf3137}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=449304}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 32
\issue 1
\pages 602--614
\crossref{https://doi.org/10.1007/BF01041434}


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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. 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
    2. 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
    3. S. A. Vugal'ter, “Asymptotic behavior of the eigenvalues of many-particle Hamiltonians on subspaces of functions of a given symmetry”, Theoret. and Math. Phys., 83:2 (1990), 502–510  mathnet  crossref  mathscinet  isi
    4. S. A. Vugal'ter, G. M. Zhislin, “The Discrete Spectrum of a Many-Particle Pseudorelativistic Hamiltonian”, Funct. Anal. Appl., 32:2 (1998), 134–136  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Simon B., “Tosio Kato'S Work on Non-Relativistic Quantum Mechanics, Part 2”, Bull. Math. Sci., 9:1 (2019), UNSP 1950005  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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