Bounds on the Elements of the Equivalent Network for Scattering in Waveguides, Vol. 1: Theory (Classic Reprint) - Tapa dura

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Excerpt from Bounds on the Elements of the Equivalent Network for Scattering in Waveguides, Vol. 1: Theory

Now a rather general approach has been devised by T. Kato for obtaining bounds on cot (n where n is the phase shift for a given angular momentum in a quantum mechanical central potential scattering problem and O is a parameter chosen for convenience. This method should be applicable to any problem which can be analysed in terms of uncoupled standing waves each of which can be characterized by one real phase shift. It is the purpose of this paper to adapt the Kato formalism to scattering by obstacles in wave guides, including the truly three dimensional problem. The problems to be considered, for reasons which will be discussed later, are subject to the following restrictions (1) The waveguide is uniform in the asymptotic region. (2) Only the dominant mode propagates, with exceptions which will be mentioned later. (5) The obstacle is symmetrical about a plane perpendicular to the axis of the waveguide. (a) The waveguide and obstacle are lossless.

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