Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

L. A. A. Nikolopoulos, J. S. Parker, K. T. Taylor

Research output: Contribution to journalArticle

31 Citations (Scopus)
204 Downloads (Pure)

Abstract

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.
Original languageEnglish
Article number063420
Number of pages12
JournalPhysical Review A
Volume78
Issue number6
DOIs
Publication statusPublished - 22 Dec 2008

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Fingerprint Dive into the research topics of 'Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case'. Together they form a unique fingerprint.

Cite this