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Teoreticheskaya i Matematicheskaya Fizika, 1973, Volume 16, Number 2, Pages 235–246 (Mi tmf3755)  

This article is cited in 22 scientific papers (total in 22 papers)

On the discrete spectrum of the Hamiltonian of an n-particle quantum system

M. A. Antonets, G. M. Zhislin, I. A. Shereshevskii
References:
Abstract: Sufficient conditions are obtained for the discrete spectrum of the energy operator of an n-particle system to be finite in the space of functions of given permutational and rotational symmetry. It is shown that under the same conditions the boundary of the continuous speetrum cannot be an eigenvalue of infinite multiplicity. For application of the basic theorem, the etgenvatues of the Schrödinger operator are investigated as functions of the coupling constant.
Received: 16.06.1972
English version:
Theoretical and Mathematical Physics, 1973, Volume 16, Issue 2, Pages 800–809
DOI: https://doi.org/10.1007/BF01037133
Bibliographic databases:
Language: Russian
Citation: M. A. Antonets, G. M. Zhislin, I. A. Shereshevskii, “On the discrete spectrum of the Hamiltonian of an n-particle quantum system”, TMF, 16:2 (1973), 235–246; Theoret. and Math. Phys., 16:2 (1973), 800–809
Citation in format AMSBIB
\Bibitem{AntZhiShe73}
\by M.~A.~Antonets, G.~M.~Zhislin, I.~A.~Shereshevskii
\paper On the discrete spectrum of the Hamiltonian of an $n$-particle quantum system
\jour TMF
\yr 1973
\vol 16
\issue 2
\pages 235--246
\mathnet{http://mi.mathnet.ru/tmf3755}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=496004}
\zmath{https://zbmath.org/?q=an:0278.47005}
\transl
\jour Theoret. and Math. Phys.
\yr 1973
\vol 16
\issue 2
\pages 800--809
\crossref{https://doi.org/10.1007/BF01037133}
Linking options:
  • https://www.mathnet.ru/eng/tmf3755
  • https://www.mathnet.ru/eng/tmf/v16/i2/p235
  • This publication is cited in the following 22 articles:
    1. B. K. Novosadov, “Forces in Molecules. New Quantum Relations”, J Struct Chem, 59:1 (2018), 11  crossref
    2. Gribov L.A., Baranov V.I., Mikhailov I.V., “Strela vremeni na rannikh stadiyakh evolyutsii biosfery. determinizm i mnozhestvennost”, Geokhimiya, 2012, no. 5, 435–435  elib
    3. Gribov L.A., “K voprosu o postanovke zadachi v obschei kvantovoi teorii spektrov mnogoatomnykh molekul”, Optika i spektroskopiya, 112:5 (2012), 710–710  elib
    4. L. A. Gribov, “Toward substantiation of a problem in the general quantum theory of spectra of polyatomic molecules”, Opt. Spectrosc., 112:5 (2012), 652  crossref
    5. Gribov L.A., Prokofeva N.I., “Matrichnye elementy dlya dipolnykh perekhodov pri postanovke kvantovoi zadachi dlya molekul s ogranicheniyami na dvizheniya yader”, Zhurnal strukturnoi khimii, 51:5 (2011), 871–878 Matrix elements for dipole transitions in the statement of the quantum problem for molecules with restrictions on nuclear motion  elib
    6. L. A. Gribov, N. I. Prokofieva, “Matrix elements for dipole transitions in the statement of the quantum problem for molecules with restrictions on nuclear motion”, J Struct Chem, 52:5 (2011), 841  crossref
    7. L. A. Gribov, V. I. Baranov, “Theory of branching bifurcation photochemical reactions”, High Energy Chem, 44:6 (2010), 462  crossref
    8. L. A. Gribov, “A new formulation of the quantum problem in the theory of spectra of polyatomic molecules”, J Appl Spectrosc, 77:1 (2010), 1  crossref
    9. Leonid M. Brekhovskikh, Oleg A. Godin, Springer Series on Wave Phenomena, 10, Acoustics of Layered Media II, 1999, 121  crossref
    10. H Hogreve, “On the maximal electronic charge bound by atomic nuclei”, J. Phys. B: At. Mol. Opt. Phys., 31:10 (1998), L439  crossref
    11. H Hogreve, “Destabilization of Atomic Anions: The case of F-and O2-”, Phys. Scr., 58:1 (1998), 25  crossref
    12. Leonid M. Brekhovskikh, Oleg A. Godin, Springer Series on Wave Phenomena, 10, Acoustics of Layered Media II, 1992, 113  crossref
    13. M. A. Antonets, I. A. Shereshevskii, L. V. Sherstneva, “Fine structure of dispersion curves for waves in a layered medium”, Radiophys Quantum Electron, 33:1 (1990), 60  crossref
    14. Jonathan D. Baker, David E. Freund, Robert Nyden Hill, John D. Morgan, “Radius of convergence and analytic behavior of the1Zexpansion”, Phys. Rev. A, 41:3 (1990), 1247  crossref
    15. W. D. Evans, Roger T. Lewis, “𝑁-body Schrödinger operators with finitely many bound states”, Trans. Amer. Math. Soc., 322:2 (1990), 593  crossref
    16. Barry Simon, Lecture Notes in Mathematics, 1159, Schrödinger Operators, 1985, 177  crossref
    17. I. M. Sigal, “Geometric methods in the quantum many-body problem. Nonexistence of very negative ions”, Commun.Math. Phys., 85:2 (1982), 309  crossref
    18. I. M. Sigal, Lecture Notes in Physics, 153, Mathematical Problems in Theoretical Physics, 1982, 149  crossref
    19. Robert Nyden Hill, “Proof that theH-Ion Has Only One Bound State”, Phys. Rev. Lett., 38:12 (1977), 643  crossref
    20. D. R. Yafaev, “On the point spectrum in the quantum-mechanical many-body problem”, Math. USSR-Izv., 10:4 (1976), 861–896  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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