Computation of the scattering amplitude in the spheroidal coordinates

The spheroidal coordinate is known to be one of the orthogonal curvilinear coordinates in which we can solve the Helmholtz equation by separation of variables. Recently it turns out that we can also solve the idealized Tonomura model (the three dimensional system in which there is an infinitesimally thin ring of magnetic solenoid), under the magnetic quantization condition. We shall explain how to calculate the generalized eigenfunction, the scattering amplitude, and give some numerical results for the obtained formulas.


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