Title
Applying numerical continuation to the parameter dependence of solutions of the Schrödinger equation Applying numerical continuation to the parameter dependence of solutions of the Schrödinger equation
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Antwerp ,
Subject
Mathematics
Source (journal)
Journal of computational and applied mathematics. - Antwerp
Volume/pages
234(2010) :4 , p. 1238-1248
ISSN
0377-0427
ISI
000278172200029
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In molecular reactions at the microscopic level, the appearance of resonances has an important influence on the reactivity. It is important to predict when a bound state transitions into a resonance and how these transitions depend on various system parameters such as internuclear distances. The dynamics of such systems are described by the time-independent Schrödinger equation and the resonances are modeled by poles of the S-matrix. Using numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, we are able to develop efficient and robust methods to study the transitions of bound states into resonances. By applying Kellers Pseudo-Arclength continuation, we can minimize the numerical complexity of our algorithm. As continuation methods generally assume smooth and well-behaving functions and the S-matrix is neither, special care has been taken to ensure accurate results. We have successfully applied our approach in a number of model problems involving the radial Schrödinger equation.
E-info
https://repository.uantwerpen.be/docman/iruaauth/3db2a7/8a4a5e6be6b.pdf
Full text (open access)
https://repository.uantwerpen.be/docman/irua/afd850/3958.pdf
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