Matrix methods for radial Schr'{o}dinger eigenproblems defined on a semi-infinite domain

摘要

In this paper, we discuss numerical approximation of the eigenvalues of theone-dimensional radial Schr\"{o}dinger equation posed on a semi-infiniteinterval. The original problem is first transformed to one defined on a finitedomain by applying suitable change of the independent variable. The eigenvalueproblem for the resulting differential operator is then approximated by ageneralized algebraic eigenvalue problem arising after discretization of theanalytical problem by the matrix method based on high order finite differenceschemes. Numerical experiments illustrate the performance of the approach.