| A combined R-matrix eigenstate basis set and finite-differences propagation method for the time-dependent Schrödinger equation: the one-elecron case |
L. A.A. Nikolopoulos, J. Parker, K. T. Taylor
Department of Applied Mathematics and Theoretical Physics
The Queen's University of Belfast, BT7 1NN Belfast,UK |
In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic systems under strong electromagnetic fields with the configuration space of the electron's coordinates separated artificially over two regions, that is region (I) and (II). In region (I) the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wavefunction. In region (II) a grid representation of the wavefunction is considered and propagation in space and time is obtained through the finite-differences method [1]. 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 the R-matrix theory [2], namely that beyond a certain distance {[}encompassing region (I)] the ejected electron is distinguishable from the other electrons and there evolves effectively as a one-electron system. The method is developed for single active electron systems with the R-matrix eigenstates expanded on a set of B-splines basis set [3] and applied to the case of the hydrogen being the ideal systems for all the unnecessary multi-electron complications to be absent.
References,
[1] K. J. Meharg, J.S. Parker and K.T. Taylor, J. Phys. B, 38,237,(2005)
[2] P. G. Burke and K. Berrington, Atomic and Molecular Processes: An R-matrix approach, (IOP Publishing, Bristol 1993)
[3] L. A.A. Nikolopoulos, Phys. Rev. A, 73, 043408, (2006) |
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