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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 4, Pages 908–948 (Mi izv2214)  

This article is cited in 7 scientific papers (total in 7 papers)

On the point spectrum in the quantum-mechanical many-body problem

D. R. Yafaev


Abstract: The paper gives a complete formulation and proof of a number of assertions regarding the point spectrum of the Schrödinger operator of a many-particle system announced earlier by the author. In particular, conditions that the discrete spectrum of this operator be finite are obtained. The results of the work are applicable to certain specific quantum systems, for example, to univalent negative atomic ions and to diatomic molecules.
Bibliography: 20 titles.

Full text: PDF file (4003 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:4, 861–896

Bibliographic databases:

UDC: 517.4+517.9
MSC: Primary 81A81, 35J10; Secondary 35P25
Received: 18.12.1974

Citation: D. R. Yafaev, “On the point spectrum in the quantum-mechanical many-body problem”, Izv. Akad. Nauk SSSR Ser. Mat., 40:4 (1976), 908–948; Math. USSR-Izv., 10:4 (1976), 861–896

Citation in format AMSBIB
\Bibitem{Yaf76}
\by D.~R.~Yafaev
\paper On the point spectrum in the quantum-mechanical many-body problem
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 4
\pages 908--948
\mathnet{http://mi.mathnet.ru/izv2214}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=757761}
\zmath{https://zbmath.org/?q=an:0344.35024}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 4
\pages 861--896
\crossref{https://doi.org/10.1070/IM1976v010n04ABEH001819}


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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, “Finiteness of the discrete spectrum of many-particle Hamiltonians in symmetry spaces”, Theoret. and Math. Phys., 32:1 (1977), 602–614  mathnet  crossref  mathscinet
    2. I. M. Sigal, “Geometric methods in the quantum many-body problem. Nonexistence of very negative ions”, Comm Math Phys, 85:2 (1982), 309  crossref  mathscinet  zmath  adsnasa
    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. E. L. Korotyaev, “On the eigenfunctions of the monodromy operator of the Schrödinger operator with a time-periodic potential”, Math. USSR-Sb., 52:2 (1985), 423–438  mathnet  crossref  mathscinet  zmath
    6. Volker Bach, Roger Lewis, Elliott H. Lieb, Heinz Siedentop, “On the number of bound states of a bosonicN-particle Coulomb system”, Math Z, 214:1 (1993), 441  crossref  mathscinet  zmath  isi
    7. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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