| A techniques of an intermediate operator is developed for the Friedrichs model obtained as a finite-dimensional perturbation [ {cal P} longrightarrow {cal P}_{_{varepsilon}} = {cal P} + varepsilon A ] of the momentum operator ${cal P} = frac{1}{i},,frac{d}{dx}$, defined by the corresponding operator-extension procedure. This technique permits to observe a creation of the resonance at the given point $k_{_{0}}$ via presenting the Scattering matrix for the above pair as a product of the non-analytic at $left(varepsilon,,kright) = left(0,,k_{_0}right)$ factor $S^{^{varepsilon}}_{_{0}} left(k right) $ which is the Scattering matrix to the pair $ left{{cal P}^{^{varepsilon}}_{_{0}},,{cal P}right}$ of the momentum with a local intermediate operator $ {cal P}^{^{varepsilon}}_{_{0}}$, and an analytic factor $ Sleft({cal P} + varepsilon A,,{cal P}^{^{varepsilon}}_{_{ 0}} right) $ of both variables $left(varepsilon,, kright)$ near the point $left(0,, k_{_0}right)$ which is the Scattering matrix of the pair $left({cal P}_{_{varepsilon}},{cal P}^{^{varepsilon}}_{_{ 0}}right)$. The corresponding representation is valid also for eigenfunctions of the perturbed operator.} vskip |
Keywords
Operator Extention , Blaschke function
Math Review Classification
Primary pacs{~03.65.Nk}
; Secondary pacs{~ 02.30.Tb}
Last Updated
10 December 2003
Length
22 pages
Availability
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