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TMF, 1982, Volume 51, Number 2, Pages 181–191 (Mi tmf2407)  

This article is cited in 10 scientific papers (total in 10 papers)

Three-body problems with $\delta$-functional potentials

Yu. G. Shondin


Abstract: Possible realizations of three-particle singular Hamiltonians corresponding to $\delta$-functional two-body potentials are described. The scheme used to describe the singular potentials is essentially the same as Shirokov's [1, 2]. It is shown that besides the classical model [3, 4] it is possible to have other sensible realizations which go beyond the space of square integrable functions but still have a semibounded Hamiltonian.

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English version:
Theoretical and Mathematical Physics, 1982, 51:2, 434–441

Bibliographic databases:

Received: 12.02.1981

Citation: Yu. G. Shondin, “Three-body problems with $\delta$-functional potentials”, TMF, 51:2 (1982), 181–191; Theoret. and Math. Phys., 51:2 (1982), 434–441

Citation in format AMSBIB
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\by Yu.~G.~Shondin
\paper Three-body problems with $\delta$-functional potentials
\jour TMF
\yr 1982
\vol 51
\issue 2
\pages 181--191
\mathnet{http://mi.mathnet.ru/tmf2407}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=672583}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 51
\issue 2
\pages 434--441
\crossref{https://doi.org/10.1007/BF01036208}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982PT76000004}


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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. Yu. G. Shondin, “Generalized pointlike interactions in $R_3$ and related models with rational $S$-matrix”, Theoret. and Math. Phys., 64:3 (1985), 937–944  mathnet  crossref  mathscinet  isi
    2. B. S. Pavlov, “Boundary conditions on thin manifolds and the semiboundedness of the three-particle Schrödinger operator with pointwise potential”, Math. USSR-Sb., 64:1 (1989), 161–175  mathnet  crossref  mathscinet  zmath
    3. A. K. Motovilov, “Algebraic version of extension theory for a quantum system with internal structure”, Theoret. and Math. Phys., 97:2 (1993), 1217–1228  mathnet  crossref  mathscinet  zmath  isi
    4. K. A. Makarov, V. V. Melezhik, A. K. Motovilov, “The point interactions in the problem of three quantum particles with internal structure”, Theoret. and Math. Phys., 102:2 (1995), 188–207  mathnet  crossref  mathscinet  zmath  isi
    5. Yu. G. Shondin, “Semibounded local hamiltonians for perturbations of the laplacian supported by curves with angle points in $\mathbb R^4$”, Theoret. and Math. Phys., 106:2 (1996), 151–166  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. K. A. Makarov, V. V. Melezhik, “The Efimov effect and collaps in three-body systems with point-like interactions. I”, Theoret. and Math. Phys., 107:3 (1996), 755–769  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Vall, AN, “Fine tuning renormalization and two-particle states in nonrelativistic four-fermion model”, International Journal of Modern Physics A, 12:28 (1997), 5039  crossref  isi
    8. V. G. Danilov, V. P. Maslov, V. M. Shelkovich, “Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems”, Theoret. and Math. Phys., 114:1 (1998), 1–42  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Kurasov P., Pavlov B., “Few-body Krein's formula”, Operator Theory and Related Topics, Operator Theory : Advances and Applications, 118, 2000, 225–254  isi
    10. Vall, AN, “Two- and three-particle states in a nonrelativistic four-fermion model in the fine-tuning renormalization scheme: Goldstone mode versus extension theory”, Few-Body Systems, 30:3 (2001), 187  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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