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

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

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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
\Bibitem{Sho82} \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
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
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
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
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
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
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
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
9. Kurasov P., Pavlov B., “Few-body Krein's formula”, Operator Theory and Related Topics, Operator Theory : Advances and Applications, 118, 2000, 225–254
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
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