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Abstract

In this thesis the Strang-splitting technique is used was a classical Monte Carlo simulation imitating quantum effects for the propagation of a hydrogen atom in a monochromatic laser field using dipole approximation. The pulse was imposed onto the atom for one full laser period. The treatment was done in 3 dimensions and without any changes to the potentials used (e.g. no soft-core potential). The main goal is to determine the ionisation probability in order to bring high intensity laser to proper use in science and technology as measurements of the intensity of high intensity laser are experimentally challenging. A comparison with a symplectic implicit and an explicit 3rd order Runge-Kutta scheme was able to show the advantages the Strang-splitting has over both Runge-Kutta schemes used. The comparison to a quantum mechanical numerical solution yielding upper bounds for the ionisation probability using the program Qprop could only partially verify the classical results obtained. However the problems that occurred are known and are not to be attributed to the Strang-splitting. In summary the magnificent performance of the Strang-splitting caused by its proterties (symplecticity symmetry-preserving, time-reversibility preservation and first order invariant preservation) could be verified and more research possibilities were proposed.