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Mathematics of the USSR-Sbornik, 1974, Volume 23, Issue 4, Pages 535–559
DOI: https://doi.org/10.1070/SM1974v023n04ABEH001730
(Mi sm3734)
 

This article is cited in 101 scientific papers (total in 101 papers)

On the theory of the discrete spectrum of the three-particle Schrödinger operator

D. R. Yafaev
References:
Abstract: We investigate the discrete spectrum of the Schrödinger operator $H$ for a system of three particles. We assume that the operators $h_\alpha$, $\alpha=1,2,3$, which describe the three subsystems of two particles do not have any negative eigenvalues. Under the assumption that either two or three of the operators $h_\alpha$ have so-called virtual levels at the start of the continuous spectrum, we establish the existence of an infinite discrete spectrum for the three-particle operator $H$. The functions which describe the interactions between pairs of particles can be rapidly decreasing (or even of compact support) with respect to $x$.
Bibliography: 17 titles.
Received: 26.11.1973
Bibliographic databases:
UDC: 517.43+517.948.35
MSC: Primary 35J10, 35P05, 45F05; Secondary 30A14, 30A86, 47B10, 47B35
Language: English
Original paper language: Russian
Citation: D. R. Yafaev, “On the theory of the discrete spectrum of the three-particle Schrödinger operator”, Math. USSR-Sb., 23:4 (1974), 535–559
Citation in format AMSBIB
\Bibitem{Yaf74}
\by D.~R.~Yafaev
\paper On the theory of the discrete spectrum of the three-particle Schr\"odinger operator
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 4
\pages 535--559
\mathnet{http://mi.mathnet.ru//eng/sm3734}
\crossref{https://doi.org/10.1070/SM1974v023n04ABEH001730}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=356752}
\zmath{https://zbmath.org/?q=an:0342.35041}
Linking options:
  • https://www.mathnet.ru/eng/sm3734
  • https://doi.org/10.1070/SM1974v023n04ABEH001730
  • https://www.mathnet.ru/eng/sm/v136/i4/p567
  • This publication is cited in the following 101 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:1006
    Russian version PDF:276
    English version PDF:38
    References:69
    First page:1
     
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