Title
Long-time solution of the time-dependent Schrödinger equation for an atom in an electromagnetic field using complex coordinate contours
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Lancaster, Pa ,
Subject
Mathematics
Physics
Chemistry
Source (journal)
Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015
Volume/pages
80(2009) :6 , p. 063419,1-063419,12
ISSN
1094-1622
1050-2947
ISI
000273233800118
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We demonstrate that exterior complex scaling (ECS) can be used to impose outgoing wave boundary conditions exactly on solutions of the time-dependent Schrödinger equation for atoms in intense electromagnetic pulses using finite grid methods. The procedure is formally exact when applied in the appropriate gauge and is demonstrated in a calculation of high-harmonic generation in which multiphoton resonances are seen for long pulse durations. However, we also demonstrate that while the application of ECS in this way is formally exact, numerical error can appear for long-time propagations that can only be controlled by extending the finite grid. A mathematical analysis of the origins of that numerical error, illustrated with an analytically solvable model, is also given.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/53ab19/50b5c4cf.pdf
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