Matrix methods for radial Schroedinger eigenproblems defined on a semi-infinite domain.

In this paper, we discuss numerical approximation of the eigenvalues of the one-dimensional radial Schr ̈odinger 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 ap- proximated 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.