The motion of a charged quantum particle in a homogeneous electric field is one of the rare examples of an analytically solvable problem in quantum mechanics in realistic three-dimensional configuration space. In the thesis, an exact expression for the propagator (energy Green function) describing this quantum ballistic motion for particles of some fixed energy emitted by a pointlike isotropic source is derived. Also, it is shown how to extend this theory to higher partial waves, thereby establishing the useful formalism of quantum multipole sources; the complete results for the ballistic problem are listed within this volume. These multipole sources are advantageously applied in the theoretical description of the quantum dynamics of electrons released from negative ions by means of the photodetachment process, i.e., ion-photon interaction, and are able to reproduce the impressive results of recent optical experiments in a straightforward manner. In particular, it has been demonstrated that quantum motion in a homogeneous external field may lead to large-scale quantum interference phenomena. The origin of this spectacular effect is traced back to the properties of classical ballistic motion by means of a semiclassical analysis of uniformly accelerated motion. Having the complete quantum solution of this modified scattering problem at hand, one may gain unprecedented insight into the properties of tunneling phenomena in three-dimensional space, a field of study with long history and notorious for its inaccessibility. Starting with the WKB approximation to ballistic tunneling motion as a guide, a conceptually simple model of multidimensional tunneling processes, the minimum uncertainty model, is developed which is based on the Heisenberg uncertainty relation and the semiclassical idea of instanton tunneling times. Despite its simplicity, this heuristic idea gives surprisingly accurate estimates for the distribution of the electron current for tunneling sources in a homogeneous force field, and delivers some insight into the properties of field emission from mesoscopic tips which have been established experimentally earlier. In recent years, the study of tunneling electron sources in three-dimensional potential barrier environments has become increasingly important with the rise of the scanning tunneling microscope (STM) as a prime tool in the experimental characterization of surfaces on an atomic scale. Quantum multipole sources provide a valuable element in the construction of a theoretical model for the electron transport through the tip-surface junction taking place in a STM apparatus. A theoretical approach to the STM based on electron sources is outlined in the thesis; it bears strong resemblance to the theory of conduction through mesoscopic point contacts that has become a field of intense research recently. Computer simulations indicate that the pictorial source model for STM despite its simplicity provides a useful tool that not only permits to illuminate the imaging mechanism of the STM and to estimate its resolution capabilities, but the results derived from it also compare favorably to experimental data obtained from simple metal surfaces.
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The motion of a charged quantum particle in a homogeneous electric field is one of the rare examples of an analytically solvable problem in quantum mechanics in realistic three-dimensional configuration space. In the thesis, an exact expression for the propagator (energy Green function) describing this quantum ballistic motion for particles of some fixed energy emitted by a pointlike isotropic source is derived. Also, it is shown how to extend this theory to higher partial waves, thereby establi...
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