Dissertationsubmitted to theCombined Faculties for the Natural Sciences and for Mathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural Sciencespresented byDiplom-Physiker Mario Verschlborn in Schw¨abisch Gmu¨ndOral examination: July 18, 2007Dispersion in laser-drivenrelativistic quantum systemsReferees: Prof. Dr. C. H. KeitelProf. Dr. O. NachtmannAbstractThewavepacketdynamicsofelectronsdrivenbystronglaserfieldsisexaminedwiththe objective to both describe and manipulate the spreading dynamics. Having estab-lishedanalytical methodsbasedoneitherclassical orquantummechanics,thequantumapproach is first applied to free, laser-driven electrons. Intuitive results are found forboth the relativistic and the nonrelativistic regime beyond the dipole approximation.In order to generalize the concept of recollisions to relativistic energies where magneticfieldeffectsareimportant,theelectrondynamicsinstandinglaserfieldswithlinearandcircular polarization are analyzed and compared. Furthermore, a novel scheme of twoconsecutive laser pulses is introduced, which allows for recollisions with the maximumelectron energy accessible in propagating laser fields. In this scheme, the Lorentz driftis employed bothtoseparate electrons from atoms or molecules andtodrivethembackfor recollisions. Aiming to increase the reaction probabilities of recollisions, two meth-ods to inverse wave packet spreading are introduced. Both approaches, i.