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arXiv · 1105.3916

Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method

Arnaud Leclerc·Georges Jolicard·John P. Killingbeck
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Abstract

The Constrained Adiabatic Trajectory Method (CATM) allows us to compute solutions of the time-dependent Schrödinger equation using the Floquet formalism and Fourier decomposition, using matrix manipulation within a non-orthogonal basis set, provided that suitable constraints can be applied to the initial conditions for the Floquet eigenstate. A general form is derived for the inherent absorbing potential, which can reproduce any dispersed boundary conditions. This new artificial potential acting over an additional time interval transforms any wavefunction into a desired state, with an error involving exponentially decreasing factors. Thus a CATM propagation can be separated into several steps to limit the size of the required Fourier basis. This approach is illustrated by some calculations for the $H_2^+$ molecular ion illuminated by a laser pulse.

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Arnaud Leclerc, Georges Jolicard, John P. Killingbeck. 2011-05-19. Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method. https://doi.org/10.1063/1.3592374

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