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arXiv · 1406.5882

Automatic computation of quantum-mechanical bound states and wavefunctions

Veerle Ledoux·Marnix Van Daele
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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.

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Veerle Ledoux, Marnix Van Daele. 2014-06-23. Automatic computation of quantum-mechanical bound states and wavefunctions. https://arxiv.org/abs/1406.5882

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