Determination of partially known Sturm–Liouville potentials

摘要

It is well known that the determination of a general potential function employs two sets of information. One or both may be a sequence of eigenvalues. In this work a partially known potential and one finite sequence of eigenvalues are given in order to approximate a non-symmetric potential. We utilize not only the finite difference method but also Numerov’s method to approximate the necessary eigenvalues in each iteration step. A complete set of eigenvalues is the main information to approximate a potential. In this paper a method recovering a missing eigenvalue in the sequence is given.