Removal of the Energy Dependence from the Resolvent-like Energy-Dependent Interactions

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dc.creatorMotovilov, A. K.
dc.date1995-05-21
dc.date1996-06-11
dc.date.accessioned2026-07-07T09:04:46Z
dc.date.available2026-07-07T09:04:46Z
dc.descriptionThe spectral problem $(A + V(z))ψ=zψ$ 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.
dc.description90 kB, LaTeX, no pictures; Final published version of the paper
dc.identifierhttps://arxiv.org/abs/nucl-th/9505030
dc.identifierhttp://arxiv.org/abs/nucl-th/9505030
dc.identifierTheor.Math.Phys. 104 (1996) 989-1007; Teor.Mat.Fiz. 104N2 (1995) 281-303
dc.identifierdoi:10.1007/BF02065979
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149497
dc.subjectNuclear Theory
dc.subjectFunctional Analysis
dc.titleRemoval of the Energy Dependence from the Resolvent-like Energy-Dependent Interactions
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