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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.
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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
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\jour Izv. Akad. Nauk SSSR Ser. Mat.
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\pages 908--948
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\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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This publication is cited in the following articles:
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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
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I. M. Sigal, “Geometric methods in the quantum many-body problem. Nonexistence of very negative ions”, Comm Math Phys, 85:2 (1982), 309
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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
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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
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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
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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
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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
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