A model for the computation of quantum billiards with arbitrary shapes

Authors:
Inci M. Erhan;H. Taseli
Affiliations:
Department of Mathematics Education, Baskent University, Ankara, Turkey;Department of Mathematics, Middle East Technical University, Ankara, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

An expansion method for the stationary Schrödinger 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.