1 results for Antoniou, I.

Analytic perturbation techniques for the Friedrichs model: Intermediate Operator
Pavlov, B.; Antoniou, I. (200312)
Report
The University of Auckland LibraryA techniques of an intermediate operator is developed for the Friedrichs model obtained as a finitedimensional 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 operatorextension 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 nonanalytic 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
View record details