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TMF, 1975, Volume 25, Number 2, Pages 185–195 (Mi tmf4063)  

This article is cited in 16 scientific papers (total in 16 papers)

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

D. R. Yafaev


Abstract: The Schrödinger operator $H$ of a three-particle system with two-body interactions in considered. Under the assumptions that two-particle subsystems do not possess any negative eigenvalues and one of the subsystems has a virtual state at the lower bound of the continuous spectrum, the proof of the finiteness of discrete spectrum of operator $H$ is performed.

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English version:
Theoretical and Mathematical Physics, 1975, 25:2, 1065–1072

Bibliographic databases:

Received: 21.02.1975

Citation: D. R. Yafaev, “On the finiteness of the discrete spectrum of the three-particle Schrödinger operator”, TMF, 25:2 (1975), 185–195; Theoret. and Math. Phys., 25:2 (1975), 1065–1072

Citation in format AMSBIB
\Bibitem{Yaf75}
\by D.~R.~Yafaev
\paper On the finiteness of the discrete spectrum of the three-particle Schr\"odinger operator
\jour TMF
\yr 1975
\vol 25
\issue 2
\pages 185--195
\mathnet{http://mi.mathnet.ru/tmf4063}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=496041}
\zmath{https://zbmath.org/?q=an:0322.35022}
\transl
\jour Theoret. and Math. Phys.
\yr 1975
\vol 25
\issue 2
\pages 1065--1072
\crossref{https://doi.org/10.1007/BF01028949}


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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, “Discrete spectrum of multifrequency quantum systems possessing no stable subsystems”, Funct. Anal. Appl., 12:3 (1978), 220–221  mathnet  crossref  mathscinet  zmath
    2. 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
    3. G. M. Zhislin, “Virtual levels of $n$-particle systems”, Theoret. and Math. Phys., 68:2 (1986), 815–823  mathnet  crossref  mathscinet  isi
    4. Zh. I. Abdullaev, S. N. Lakaev, “Finiteness of discrete spectrum of three particle Schrödinger operator on the lattice”, Theoret. and Math. Phys., 111:1 (1997), 467–479  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. S. N. Lakaev, S. M. Samatov, “Finiteness of the Discrete Spectrum of the Hamiltonian of a System of Three Arbitrary Particles on a Lattice”, Theoret. and Math. Phys., 129:3 (2001), 1655–1668  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. S. N. Lakaev, S. M. Samatov, “Conditions for the finiteness of the discrete spectrum of the Hamiltonian of a system of three arbitrary particles on a lattice”, Russian Math. Surveys, 57:1 (2002), 150–152  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Albeverio, S, “On the finiteness of the discrete spectrum of four-particle lattice Schrodinger operators”, Reports on Mathematical Physics, 51:1 (2003), 43  crossref  isi
    8. Zh. I. Abdullaev, “Finiteness of discrete spectra for nontrivial values of the full quasi-momentum in the system of three bosons on a lattice”, Russian Math. Surveys, 62:1 (2007), 175–177  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. T. H. Rasulov, “Discrete spectrum of a model operator in Fock space”, Theoret. and Math. Phys., 152:3 (2007), 1313–1321  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. M. I. Muminov, A. M. Hurramov, “Spectral properties of a two-particle Hamiltonian on a lattice”, Theoret. and Math. Phys., 177:3 (2013), 1693–1705  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Gridnev D.K., “Why There Is No Efimov Effect for Four Bosons and Related Results on the Finiteness of the Discrete Spectrum”, J. Math. Phys., 54:4 (2013), 042105  crossref  isi
    12. T. Kh. Rasulov, R. T. Mukhitdinov, “The finiteness of the discrete spectrum of a model operator associated with a system of three particles on a lattice”, Russian Math. (Iz. VUZ), 58:1 (2014), 52–59  mathnet  crossref
    13. M. I. Muminov, A. M. Hurramov, “Multiplicity of virtual levels at the lower edge of the continuous spectrum of a two-particle Hamiltonian on a lattice”, Theoret. and Math. Phys., 180:3 (2014), 1040–1050  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    14. M. I. Muminov, A. M. Khurramov, “On compact distribution of two-particle Schrödinger operator on a lattice”, Russian Math. (Iz. VUZ), 59:6 (2015), 18–22  mathnet  crossref
    15. Rasulov T.H., “on the Finiteness of the Discrete Spectrum of a 3 X 3 Operator Matrix”, Methods Funct. Anal. Topol., 22:1 (2016), 48–61  mathscinet  zmath  isi
    16. Lakaev S.N. Lakaev Sh.S., “The Existence of Bound States in a System of Three Particles in An Optical Lattice”, J. Phys. A-Math. Theor., 50:33 (2017), 335202  crossref  isi
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