Title
Numerical continuation of resonances and bound states in coupled channel Schrödinger equations Numerical continuation of resonances and bound states in coupled channel Schrödinger equations
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Physics
Computer. Automation
Source (journal)
Communications in computational physics
Volume/pages
11(2012) , p. 435-455
ISSN
1815-2406
1991-7120
ISI
000301924300012
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, to the problem of tracing the parameter dependence of bound and resonant states of the quantum mechanical Schrodinger equation. We extend previous work on the subject [1] to systems of coupled equations. Bound and resonant states of the Schrodinger equation can be determined through the poles of the S-matrix, a quantity that can be derived from the asymptotic form of the wave function. We introduce a regularization procedure that essentially transforms the S-matrix into its inverse and improves its smoothness properties, thus making it amenable to numerical continuation. This allows us to automate the process of tracking bound and resonant states when parameters in the Schrodinger equation are varied. We have applied this approach to a number of model problems with satisfying results.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/901afb/4508.pdf
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