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L. Aceto, C. Magherini, E. Weinmüller:
"Matrix methods for radial Schrödinger eigenproblems defined on a semi-infinite domain";
in: "ASC Report 01/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 11.

In this paper, we discuss numerical approximation of the eigenvalues of the one-dimensional radial Schrödinger equation posed on a semi-infinite interval. The original problem is first transformed to one defined on a finite domain by applying suitable change of the independent variable. The eigenvalue problem for the resulting differential operator is then approximated by a generalized algebraic eigenvalue problem arising after discretization of the analytical problem by the matrix method based on high order finite difference schemes. Numerical experiments illustrate the performance
of the approach.

Radial Schrödinger equation, Infinite domain, Eigenvalues, Finite difference schemes

http://www.asc.tuwien.ac.at/preprint/2014/asc01x2014.pdf