New Method for Solving Eigenvalue Problems

Abstract

A new method of solving eigenvalue problems is proposed. The secular equation is represented in the form of a dispersion relation. Three methods of solving the dispersion relation are given. Several examples including both nondegenerate cases and degenerate cases are presented. All these examples demonstrate that the present treatment is better than other conventional perturbation treatments. The transformation coefficients between the unperturbed wavefunctions and the perturbed ones are given in terms of the eigenvalues thus obtained. The wavefunctions of the perturbed states form a complete orthonormal set if those of the unperturbed one do.