### Abstract

Original language | English |
---|---|

Article number | 063420 |

Number of pages | 12 |

Journal | Physical Review A |

Volume | 78 |

Issue number | 6 |

DOIs | |

Publication status | Published - 22 Dec 2008 |

### Fingerprint

### Cite this

*Physical Review A*,

*78*(6), [063420]. https://doi.org/10.1103/PhysRevA.78.063420

}

*Physical Review A*, vol. 78, no. 6, 063420. https://doi.org/10.1103/PhysRevA.78.063420

**Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case.** / Nikolopoulos, L. A. A.; Parker, J. S.; Taylor, K. T.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

AU - Nikolopoulos, L. A. A.

AU - Parker, J. S.

AU - Taylor, K. T.

PY - 2008/12/22

Y1 - 2008/12/22

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevA.78.063420

DO - 10.1103/PhysRevA.78.063420

M3 - Article

VL - 78

JO - Physical Review A (Atomic, Molecular, and Optical Physics)

JF - Physical Review A (Atomic, Molecular, and Optical Physics)

SN - 1050-2947

IS - 6

M1 - 063420

ER -