 0362 Sergej A. Choroszavin ( sergius@pve.vsu.ru )
 An Interaction of An Oscillator with
An OneDimensional Scalar Field.
Simple Exactly Solvable Models based on
Finite Rank Perturbations Methods.
II: Resolvents formulae
(66K, LaTeX 2.09)
Feb 14, 03

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Abstract. 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 +\Omega^2 q \Omega^2<l_2 u> =w_1 ,
z u +4\gamma_c\delta_{\alpha,x_0}q Bu
+4\gamma_c\delta_{\alpha,x_0}<l_2 u> =w_2.
Besides, less detailed discussion of related models.
Central mathematical points:
Finite Rank Perturbations Methods, Resolvents formulae,
Donoghuelike models, Friedrichslike models.
Central physical points: phenomenon of Resonance
and notion of Second Sheet.
Hereafter I use a P.A.M. Dirac's ``braket'' syntax and suppose that
$B$ stands for an abstract linear operator,
$l$ for a linear functional, $u, w_2, \delta_{\alpha,x_0}$
for abstract elements; $q, w_1 z, \Omega, \gamma_c$ stand for numbers.
$q, u$ are objects to be found, the others are arbitrarily given.
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