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TMF, 1995, Volume 104, Number 2, Pages 281–303 (Mi tmf1338)  

This article is cited in 2 scientific papers (total in 2 papers)

Removal of the dependence on energy from interactions depending on it as a resolvent

A. K. Motovilov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: The spectral problem $(A + V(z))\psi =z\psi$ is considered with $A$, a self-adjoint Hamiltonian of sufficiently arbitrary nature. The perturbation $V(z)$ is assumed to depend on the energy $z$ as resolvent of another self-adjoint operator $A':$ $V(z)=-B(A'-z)^{-1}B^{*}$. It is supposed that operator $B$ has a finite Hilbert–Schmidt norm and spectra of operators $A$ and $A'$ are separated. The conditions are formulated when the perturbation $V(z)$ may be replaced with an energy-independent “potential” $W$ such that the Hamiltonian $H=A +W$ has the same spectrum (more exactly a part of spectrum) and the same eigenfunctions as the initial spectral problem. The orthogonality and expansion theorems are proved for eigenfunction systems of the Hamiltonian $ H=A + W$. Scattering theory is developed for $H$ in the case when operator $A$ has continuous spectrum. Applications of the results obtained to few-body problems are discussed.

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English version:
Theoretical and Mathematical Physics, 1995, 104:2, 989–1007

Bibliographic databases:

Received: 06.09.1994

Citation: A. K. Motovilov, “Removal of the dependence on energy from interactions depending on it as a resolvent”, TMF, 104:2 (1995), 281–303; Theoret. and Math. Phys., 104:2 (1995), 989–1007

Citation in format AMSBIB
\Bibitem{Mot95}
\by A.~K.~Motovilov
\paper Removal of the dependence on energy from interactions depending on it as a resolvent
\jour TMF
\yr 1995
\vol 104
\issue 2
\pages 281--303
\mathnet{http://mi.mathnet.ru/tmf1338}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1488675}
\zmath{https://zbmath.org/?q=an:0856.47044}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 104
\issue 2
\pages 989--1007
\crossref{https://doi.org/10.1007/BF02065979}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UD33400007}


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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. A. Yu. Konstantinov, “Spectral Analysis of One Class of Matrix Differential Operators”, Funct. Anal. Appl., 31:3 (1997), 209–211  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Hardt, V, “A factorization theorem for the transfer function associated with a 2 x 2 operator matrix having unbounded couplings”, Journal of Operator Theory, 48:1 (2002), 187  mathscinet  zmath  isi
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