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TMF, 1985, Volume 65, Number 1, Pages 24–34 (Mi tmf5050)  

This article is cited in 4 scientific papers (total in 4 papers)

Generalized pointlike interactions in $R_3$ and related models with rational $S$ matrix II. $l=1$

Yu. G. Shondin


Abstract: A description is given of “inequivalen” Hamiltonians on a Hilbert space $\mathfrak{H}^N$ which is obtained by restricting the Pontryagin space of the form
$$ \Pi_1^N=\mathscr{H}_{+}^N[+]\mathscr{H}_{-},\quad\mathscr{H}_{+}^N=L_2(R_3)\oplus C_{N+1}\quad\mathscr{H}_{-}=C_1 $$
to a hyperplane of unit codimensionality, the Hamiltonians leading to a rational $S$ matrix in the sense of scattering theory in the pair of spaces $L_2$ and $\mathfrak{H}^N$. The use in intermediate considerations of spaces with indefinite metric is an essential and distinctive feature of the ease considered. Hamiltonians on $\mathfrak{H}^1$ are characterized as models of generalized pointlike interactions.

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English version:
Theoretical and Mathematical Physics, 1985, 65:1, 985–992

Bibliographic databases:

Received: 18.07.1984

Citation: Yu. G. Shondin, “Generalized pointlike interactions in $R_3$ and related models with rational $S$ matrix II. $l=1$”, TMF, 65:1 (1985), 24–34; Theoret. and Math. Phys., 65:1 (1985), 985–992

Citation in format AMSBIB
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\by Yu.~G.~Shondin
\paper Generalized pointlike interactions in $R_3$ and related models with rational $S$ matrix II.~$l=1$
\jour TMF
\yr 1985
\vol 65
\issue 1
\pages 24--34
\mathnet{http://mi.mathnet.ru/tmf5050}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=822210}
\transl
\jour Theoret. and Math. Phys.
\yr 1985
\vol 65
\issue 1
\pages 985--992
\crossref{https://doi.org/10.1007/BF01028631}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1985C731200003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. S. Pavlov, “The theory of extensions and explicitly-soluble models”, Russian Math. Surveys, 42:6 (1987), 127–168  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Yu. G. Shondin, “Quantum-mechanical models in $R_n$ associated with extensions of the energy operator in a Pontryagin space”, Theoret. and Math. Phys., 74:3 (1988), 220–230  mathnet  crossref  mathscinet  zmath  isi
    3. V. A. Derkach, “Extensions of Laguerre operators in indefinite inner product spaces”, Math. Notes, 63:4 (1998), 449–459  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Shvedov, OY, “Exactly solvable quantum mechanical models with infinite renormalization of the wavefunction”, Journal of Physics A-Mathematical and General, 34:16 (2001), 3483  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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