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A model for the computation of quantum billiards with arbitrary shapes

Erhan, Inci M.
Taşeli, Hasan
An expansion method for the stationary Schrodinger equation of a three-dimensional quantum billiard system whose boundary is defined by an arbitrary analytic function is introduced. The method is based on a coordinate transformation and an expansion in spherical harmonics. The effectiveness is verified and confirmed by a numerical example, which is a billiard system depending on a parameter.