2003/02/15 by Sergej A. Choroszavin, Choroszavin, Sergej A.
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0302038
Latex 2.09, minor changes of the style, bibliography corrected
openalex publication_date 2003/02/15 · arxiv created 2003/03/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This 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 +Ω2 q -Ω2 =w1, z u +4γcδα,x0q -Bu +4γcδα,x0 =w2. 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, w2, δα,x0 for abstract elements; q, w1 z, Ω, γc stand for numbers. q, u are objects to be found, the others are arbitrarily given.