Piecewise constant perturbation methods for the multichannel schrödinger equation

Authors:
Veerle Ledoux;Marnix Van Daele;Guido Vanden Berghe
Affiliations:
Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Gent, Belgium;Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Gent, Belgium;Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Gent, Belgium
Venue:
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Year:
2006

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Abstract

The CPM{P,N} methods form a class of methods specially devised for the propagation of the solution of the one-dimensional Schrödinger equation. Using these CPM{P,N} methods in a shooting procedure, eigenvalues of the boundary value problem are obtained to very high precision. Some recent advances allowed the generalization of the CPM{P,N} methods to systems of coupled Schrödinger equations. Also for these generalised CPM{P,N} methods a shooting procedure can be formulated, solving the multichannel bound state problem.