Energy Correction Method Research Articles

Eigenvalue correction estimates for the one-dimensional Schrödinger equation

The problem of solving the Schrödinger equation and the more general Sturm-Liouville problem in the finite-difference approximation is considered with emphasis on the question of where to match inward and outward solutions. It is shown that the determination of the matching point is a variational problem. A modification of the usual energy correction method in which previously calculated eigenfunctions are projected out of the trial solution is described. An iterative scheme which should determine all eigenvalues below some prescribed upper limit is proposed, and its application in two sample cases is discussed.