Title 



Numerical continuation of bound and resonant states of the twochannel Schrödinger equation
 
Author 



 
Abstract 



Resonant solutions of the quantum Schrodinger equation occur at complex energies where the S matrix becomes singular. Knowledge of such resonances is important in the study of the underlying physical system. Often the Schrodinger equation depends on some parameter and one is interested in following the path of the resonances in the complex energy plane as the parameter changes. This is particularly true in coupledchannel systems where the resonant behavior is highly influenced by the strength of the channel coupling, the energy separation of the channels, and other factors. In previous work it was shown that numerical continuation, a technique familiar in the study of dynamical systems, can be brought to bear on the problem of following the resonance path in onedimensional problems [J. Broeckhove, P. Klosiewicz, and W. Vanroose, J. Comput. Appl. Math. 234, 1238 (2010).] and multichannel problems without energy separation between the channels [P. Klosiewicz, J. Broeckhove, and W. Vanroose, Commun. Comput. Phys. 11, 435 (2012).]. A regularization can be defined that eliminates coalescing poles and zeros that appear in the S matrix at the origin due to symmetries. Following the zeros of this regularized function then traces the resonance path. In this work we show that this approach can be extended to channels with energy separation, albeit limited to two channels. The issue here is that the energy separation introduces branch cuts in the complex energy domain that need to be eliminated with a socalled uniformization. We demonstrate that the resulting approach is suitable for investigating resonances in twochannel systems and provide an extensive example.   
Language 



English
 
Source (journal) 



Physical review : A : atomic, molecular and optical physics.  Lancaster, Pa, 1990  2015  
Publication 



Lancaster, Pa : 2012
 
ISSN 



10941622 [online]
10502947 [print]
 
Volume/pages 



85:1(2012), p. 012709,1012709,12
 
Article Reference 



012709
 
ISI 



000299421800004
 
Medium 



Eonly publicatie
 
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