Some finite difference methods for computing eigenvalues and eigenvectors of special two-point boundary value problems (Q1097655)

The authors consider a numerical method for the one-dimensional Schrödinger equation with even potential function. In a preceding work of the first two authors [J. Phys. A 18, 3355-3363 (1985; Zbl 0584.65055)] numerical results were presented by using the second order central difference formula for the eigenproblem. Here the authors propose the application of the sixth order central difference formula which implies a heptadiagonal coefficient matrix. To solve this algebraic eigenvalue problem, they transform the matrix into a symmetric one by similarity transformation. Then the Householder transformation gives a symmetric tridiagonal matrix. Some numerical examples, which originate in physical models, are given.