An Interaction of An Oscillator with An One-Dimensional Scalar Field. Simple Exactly Solvable Models based on Finite Rank Perturbations Methods. I: D'Alembert-Kirchhoff-like formulae

摘要

This paper is an electronic application to my set of lectures,subject:`Formal methods in solving differential equations and constructingmodels of physical phenomena'. Addressed, mainly: postgraduates and relatedreaders. Content: a very detailed discussion of the simple model of interaction basedon the equation array: d^2 q(t)/dt^2 =-\Omega^2(q(t)-Q(t))+f_0(t),d^2u(t,x)/t^2=c^{2}d^2 u(t,x)/dx ^2 -4\gamma c\delta(x-x_0)(Q(t)-q(t))+f_1(t,x), Q(t) = u(t,x_0) . Besides, less detailed discussion of relatedmodels. Central mathematical points: d'Alembert-Kirchhoff-like formulae.Central physical points: phenomena of Radiation Reaction, Braking Radiation andResonance.