%0 Journal Article %1 Wijn2007 %A de Wijn, Astrid S. %A K�mmel, Stephan %A Lein, Manfred %D 2007 %J Journal of Computational Physics %K Schr�dinger Time-dependent equation %N 1 %P 89 - 103 %R DOI: 10.1016/j.jcp.2007.03.022 %T Numerical aspects of real-space approaches to strong-field electron dynamics %U http://www.sciencedirect.com/science/article/B6WHY-4NFR5KF-2/2/601b5a21bf989d82688ad44a0399933a %V 226 %X Numerical methods for calculating strong-field, nonperturbative electron dynamics are investigated. Two different quantum-mechanical approaches are discussed: the time-dependent Schr�dinger equation and time-dependent density functional theory. We show that when solving the time-dependent Schr�dinger equation, small errors in the initial ground-state wave function can be magnified considerably during propagation. A scheme is presented to efficiently obtain the ground state with high accuracy. We further demonstrate that the commonly-used absorbing boundary conditions can severely influence the results. The requirements on the boundary conditions are somewhat less stringent in effective single-particle approaches such as time-dependent density functional theory. We point out how results from accurate wave-function based calculations can be used to improve the density functional description of long-ranged, nonlinear electron dynamics. We present details of a method to reconstruct, numerically, the full, unapproximated, Kohn-Sham potential from the density and current of the exact system.

@article{Wijn2007, abstract = {Numerical methods for calculating strong-field, nonperturbative electron dynamics are investigated. Two different quantum-mechanical approaches are discussed: the time-dependent Schr�dinger equation and time-dependent density functional theory. We show that when solving the time-dependent Schr�dinger equation, small errors in the initial ground-state wave function can be magnified considerably during propagation. A scheme is presented to efficiently obtain the ground state with high accuracy. We further demonstrate that the commonly-used absorbing boundary conditions can severely influence the results. The requirements on the boundary conditions are somewhat less stringent in effective single-particle approaches such as time-dependent density functional theory. We point out how results from accurate wave-function based calculations can be used to improve the density functional description of long-ranged, nonlinear electron dynamics. We present details of a method to reconstruct, numerically, the full, unapproximated, Kohn-Sham potential from the density and current of the exact system.}, added-at = {2010-01-22T12:15:18.000+0100}, author = {de Wijn, Astrid S. and K�mmel, Stephan and Lein, Manfred}, biburl = {https://www.bibsonomy.org/bibtex/2aed6ba3d821cae2318ecdbce14d52688/myrta}, description = {Time dependent density functional theory; Memory effects kernel; breakdown adiabatic approximation}, doi = {DOI: 10.1016/j.jcp.2007.03.022}, file = {:/home/cfc/myrta/VirtualLibrary/MemoryKernel/JCompPhys226_89_2007.pdf:PDF}, interhash = {8671f42cb7ff188974973dc557b5f617}, intrahash = {aed6ba3d821cae2318ecdbce14d52688}, issn = {0021-9991}, journal = {Journal of Computational Physics}, keywords = {Schr�dinger Time-dependent equation}, number = 1, pages = {89 - 103}, timestamp = {2010-01-22T12:15:23.000+0100}, title = {Numerical aspects of real-space approaches to strong-field electron dynamics}, url = {http://www.sciencedirect.com/science/article/B6WHY-4NFR5KF-2/2/601b5a21bf989d82688ad44a0399933a}, volume = 226, year = 2007 }