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The Constrained Adiabatic Trajectory Method (CATM) allows us to computesolutions of the time-dependent Schr\"odinger equation using the Floquetformalism and Fourier decomposition, using matrix manipulation within anon-orthogonal basis set, provided that suitable constraints can be applied tothe initial conditions for the Floquet eigenstate. A general form is derivedfor the inherent absorbing potential, which can reproduce any dispersedboundary conditions. This new artificial potential acting over an additionaltime interval transforms any wavefunction into a desired state, with an errorinvolving exponentially decreasing factors. Thus a CATM propagation can beseparated into several steps to limit the size of the required Fourier basis.This approach is illustrated by some calculations for the $H_2^+$ molecular ionilluminated by a laser pulse.

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