These are some notes about proximity resonances. Everything is done within the context of the point scatterer model. Both the 2D and 3D cases are treated. Also, a derivation of the partial wave expansion for the scattering amplitude of an arbitrary number of point scatterers is given. Everything is analytic, except for a matrix inversion step. LaTeX format
Here are some notes about incorporating higher partial waves into the point scatterer model. I show how partial waves up to any order can be included in the model. With this method, the multiple scattering of any number of finite range, non-overlapping potentials can be calculated, at any incident energy. The method requires the inversion of a matrix of dimension N(2L+1), where N is the number of potentials and L is the highest partial wave. So of course there are limits to how large a problem can be considered. LaTeX format Here's a figure that is used in the notes.
Here's a copy of my thesis, which is called "Scattering Resonances in the Extreme Quantum Limit," finished August 1999.
If you don't know how to process LaTeX documents, send me and email and I will send you a postscript version of what you want.
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