Year: 2012
Communications in Computational Physics, Vol. 11 (2012), Iss. 2 : pp. 435–455
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 Schrödinger equation. We extend previous work on the subject [1] to systems of coupled equations. Bound and resonant states of the Schrödinger 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 Schrödinger equation are varied. We have applied this approach to a number of model problems with satisfying results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.121209.050111s
Communications in Computational Physics, Vol. 11 (2012), Iss. 2 : pp. 435–455
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
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Numerical continuation of bound and resonant states of the two-channel Schrödinger equation
Kłosiewicz, P.
Vanroose, W.
Broeckhove, J.
Physical Review A, Vol. 85 (2012), Iss. 1
https://doi.org/10.1103/PhysRevA.85.012709 [Citations: 1]