Long-time solution of the time-dependent Schrödinger equation for an atom in an electromagnetic field using complex coordinate contoursLong-time solution of the time-dependent Schrödinger equation for an atom in an electromagnetic field using complex coordinate contours
Faculty of Sciences. Mathematics and Computer Science

Applied mathematics and numerical analysis

article

2009Lancaster, Pa, 2009

Mathematics

Physics

Chemistry

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

80(2009):6, p. 063419,1-063419,12

1094-1622

1050-2947

000273233800118

E

English (eng)

University of Antwerp

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.

https://repository.uantwerpen.be/docman/irua/53ab19/50b5c4cf.pdf

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