
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 selfadjoint Hamiltonian of sufficiently arbitrary nature. The perturbation $V(z)$ is assumed to depend on the energy $z$ as resolvent of another selfadjoint 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 energyindependent “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 fewbody problems are discussed.
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Theoretical and Mathematical Physics, 1995, 104:2, 989–1007
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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
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\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 281303
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\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 104
\issue 2
\pages 9891007
\crossref{https://doi.org/10.1007/BF02065979}
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A. Yu. Konstantinov, “Spectral Analysis of One Class of Matrix Differential Operators”, Funct. Anal. Appl., 31:3 (1997), 209–211

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

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