Automatic computation of quantum-mechanical bound states and wavefunctions
Numerical Analysis
2014-06-24 v1
Abstract
We discuss the automatic solution of the multichannel Schr\"odinger equation. The proposed approach is based on the use of a CP method for which the step size is not restricted by the oscillations in the solution. Moreover, this CP method turns out to form a natural scheme for the integration of the Riccati differential equation which arises when introducing the (inverse) logarithmic derivative. A new Pr\"ufer type mechanism which derives all the required information from the propagation of the inverse of the log-derivative, is introduced. It improves and refines the eigenvalue shooting process and implies that the user may specify the required eigenvalue by its index.
Cite
@article{arxiv.1406.5882,
title = {Automatic computation of quantum-mechanical bound states and wavefunctions},
author = {Veerle Ledoux and Marnix Van Daele},
journal= {arXiv preprint arXiv:1406.5882},
year = {2014}
}