OSCILLATION THEORY AND COMPUTATIONAL PROCEDURES FOR MATRIX STURM-LIOUVILLE EIGENVALUE PROBLEMS WITH AN APPLICATION TO HYDROGEN MOLECULAR ION

A generalized Prufer transformation is used to derive comparison and oscillation theorems for the matrix Sturm-Liouville eigenvalue problem. It is shown in particular that if the eigenvectors are required to vanish at one (at least) of the end points, then the eigenvalues are uniquely characterized by the number of points (termed focal points) at which a certain determinant (of linearly independent solutions each satisfying the other boundary condition) vanishes. Simple but effective computational procedures based on this analysis are suggested, and their use is illustrated by a single-centre calculation on the 3s sigma state of the hydrogen molecular ion.