An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes
Abstract: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.
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