Abstract:
We present the analytical solution in closed form for the semiclassical limit of the quantum mechanical Coulomb Green function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and which allows us to treat the system as an essentially one dimensional problem. The semiclassical result assumes a simple analytical form and is well suited for a numerical evaluation. The method can also be extended to classically forbidden space regions. Already for moderately large principal quantum numbers nu >= 5, the semiclassical Green function is found to be an excellent approximation to the quantum mechanical Green function.

Abstract:
An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and introduce pointlike multipole sources as their limiting case. Partial wave theory is recovered for freely propagating particles. We obtain novel results for ballistic scattering in an external uniform force field, where we provide analytical solutions for both the scattering waves and the integrated particle flux. Our theory directly applies to p-wave photodetachment in an electric field. Furthermore, illustrating the effects of extended sources, we predict some properties of vortex-bearing atom laser beams outcoupled from a rotating Bose-Einstein condensate under the influence of gravity.

Abstract:
Laser-atom interaction can be an efficient mechanism for the production of coherent electrons. We analyze the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field--induced quantum mechanical drift motion of i) single electrons and ii) a dilute Fermi gas of electrons. The method yields the drift current and, at the same time it allows us to quantitatively establish the broadening of the (magnetic) Landau levels due to the electric field: Level number k is split into k+1 sublevels that render the $k$th oscillator eigenstate in energy space. Adjacent Landau levels will overlap if the electric field exceeds a critical strength. Our observations are relevant for quantum Hall configurations whenever electric field effects should be taken into account.

Abstract:
We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symmetry axis. There, four classical paths interfere. With increasing electron energy, the current distribution changes from a quantum regime governed by the uncertainty principle, to an intricate spatial pattern that yields to a semiclassical analysis.

Abstract:
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are introduced into the Schr\"odinger equation. The source formalism yields direct access to the scattering wave function, particle distribution, and total current. As an example, we study emission from three-dimensional Gaussian sources into a homogeneous force field. This model describes the behaviour of an atom laser supplied by an ideal Bose-Einstein condensate under the influence of gravity. We predict a strong dependence of the beam profile on the condensate size and the presence of interference phenomena recently observed in photodetachment experiments.

Abstract:
Progress in manufacturing technology has allowed us to probe the behavior of devices on a smaller and faster scale than ever before. With increasing miniaturization, quantum effects come to dominate the transport properties of these devices, between collisions, carriers undergo ballistic motion under the influence of local electric and magnetic fields. The often surprising propertiesof quantum ballistic transport are currently elucidated in clean atomic physics experiments. From a theoretical viewpoint, theelectron dynamics is governed by ballistic propagators and Green functions, intriguing quantities at the crossroads of classical and quantum mechanics. Here, we briefly describe the propagator method, some ballistic Green functions, and their application in a diverse range of problems in atomic and solid state physics, such as photodetachment, atom lasers, scanning tunneling microscopy, and the quantum Hall effect.

Abstract:
Many soils in the western U.S.A. contain one or several carbonate-enriched zones (CEZ). Their carbonate admixture is often attributed to steady eolian influx, with intermittent leaching episodes of variable intensity leading to pedogenic enrichment at various depths. This hypothesis would require carbonate contents to decrease and depths to those horizons to increase with elevation. Here I compute correlations for the upper three CEZ of the surface soil and of up to two buried soils between elevation, carbonate content, depth to horizon, and particle-size distribution to test for elevation- dependent trends. Actually, carbonate-content decreases with elevation indicate such trends exist and can be determined with this approach. However, some significant relationship of elevation and depth to CEZ is not supported by the data. Furthermore, influence of local carbonate on CEZ in the surface soils calls for lateral translocation. Gravelly, now-buried sediments collected eolian carbonate better than finer ones, which finding implies these sediments were at the surface once and fossilized later. Altogether, the data indicate cyclical evolution: Several cycles of the formation of colluvial slope deposits with admixed carbonate-bearing loess particles were each followed by pedogenic translocation of the carbonate just to the depth of the next parent-material disconformity. Thus, disconformities are major triggers of soil-carbonate accumulation.

Abstract:
Atoms and negative ions interacting with laser photons yield a coherent source of photoelectrons. Applying external fields to photoelectrons gives rise to interesting and valuable interference phenomena. We analyze the spatial distribution of the photocurrent using elementary quantum methods. The photoelectric effect is shown to be an interesting example for the use of coherent particle sources in quantum mechanics.

Abstract:
This paper extends and surveys some basic quality-ladder models of
education, innovation and trade in order to explain the dynamics of
technological change and aggregate growth in developed countries. We analyze
how the stochastic processes of innovation and export adaptation are affected
by asymmetric factor endowments, transport costs, and barriers to entry in
foreign markets. We show that the country-specific innovation rates are
permanently increasing in the effectiveness of education and the countries’
relative endowment with labor. Trade liberalization leads to a temporary
increase in the innovation rates but to a permanent increase in the rates of
export adaptation.

Abstract:
The paper dealt with quantum canonical ensembles by random walks, where state transitions are triggered by the connections between labels, not by elements, which are transferred. The balance conditions of such walks lead to emission rates of the labels. The labels with emission rates definitely lower than 1 are like modes. For labels with emission rates very close to 1, the quantum numbers are concentrated around a mean value. As an application I consider the role of the zero label in a quantum gas in equilibrium.