A numerical procedure to solve the multichannel Schrödinger eigenvalue problem

We discuss the numerical solution of eigenvalue problems for systems of (regular) coupled Schrödinger equations. Using a high order CPM (abbreviation for piecewise Constant (reference potential) Perturbation Method) in a shooting procedure, eigenvalues can be computed accurately. A generalization of the Prüfer method for scalar Sturm–Liouville problems makes the whole procedure more robust and allows us to specify the required eigenvalue by its index.