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

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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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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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
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
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
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
5. Simon B., “Tosio Kato'S Work on Non-Relativistic Quantum Mechanics, Part 2”, Bull. Math. Sci., 9:1 (2019), UNSP 1950005
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