An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes
نویسنده
چکیده
A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid. Keywords— Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics.
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