Abstract
A finite element package is presented that is able to treat two-dimensional Schroedinger equation problems over a finite region with an arbitrary potential and homogeneous boundary conditions. In order to present the applicability and accuracy of this approach, two cases for which the exact solution is known are solved: (i) a free particle in a spherical box, (ii) a hydrogen atom enclosed in a finite sphere. The results definitely indicate that the finite element method is both accurate and efficient and could serve as a useful tool in various single particle quantum mechanical problems.
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