An Interaction of An Oscillator with An One-Dimensional Scalar Field. Simple Exactly Solvable Models based on Finite Rank Perturbations Methods. II: Resolvents formulae

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dc.creatorChoroszavin, Sergej A.
dc.date2003-02-15
dc.date2003-03-16
dc.date.accessioned2026-07-07T04:29:48Z
dc.date.available2026-07-07T04:29:48Z
dc.descriptionThis paper is an electronic application to my set of lectures, subject:`Formal methods in solving differential equations and constructing models of physical phenomena'. Addressed, mainly: postgraduates and related readers. Content: a very detailed discussion of the simple model of interaction based on the equation array: z q +Ω^2 q -Ω^2<l|_2 u> =w_1, z u +4γ_cδ_{α,x_0}q -Bu +4γ_cδ_{α,x_0}<l|_2 u> =w_2. Besides, less detailed discussion of related models. Central mathematical points: Finite Rank Perturbations Methods, Resolvents formulae, Donoghue-like models, Friedrichs-like models. Central physical points: phenomenon of Resonance and notion of Second Sheet. Hereafter I use a P.A.M. Dirac's ``bra-ket'' syntax and suppose that $B$ stands for an abstract linear operator, $l$ for a linear functional, $u, w_2, δ_{α,x_0}$ for abstract elements; $q, w_1 z, Ω, γ_c$ stand for numbers. $q, u$ are objects to be found, the others are arbitrarily given.
dc.descriptionLatex 2.09, minor changes of the style, bibliography corrected
dc.identifierhttps://arxiv.org/abs/math-ph/0302038
dc.identifierhttp://arxiv.org/abs/math-ph/0302038
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57292
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.titleAn Interaction of An Oscillator with An One-Dimensional Scalar Field. Simple Exactly Solvable Models based on Finite Rank Perturbations Methods. II: Resolvents formulae
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