Matter waves originating from a localized region in space appear commonly in physics. Examples are photo-electrons, ballistic electrons in nanotechnology devices (scanning-tunneling microscopy, quantum Hall effect), or atoms released from a coherent source (atom laser). We introduce the energy-dependent Green function as a suitable tool to calculate the arising currents. For some systems experimental data is available and in excellent agreement with the presented results.

We provide an elementary case study of field-induced quantum tunneling in a realistic three-dimensional environment which exhibits both tunneling and classically allowed motion. An analytic description is presented for ballistic motion in a uniform electric field. From there we derive simple expressions concerning the wave function for field emission from an ultrathin quantum well in the tunneling limit. At the same time a wave-packet description of the tunneling process is obtained. The tunneling time can be read off from the lateral spread of the tunneling current distribution.

An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schrödinger 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. PACS numbers. 03.65.Nk -Scattering theory 03.75.-b -Matter waves 03.75.Fi -Phase coherent atomic ensembles; quantum condensation phenomena 32.80.Gc -Photodetachment of atomic negative ions *

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 fieldinduced 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 kth 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.Introduction. -Two-path interference along classical trajectories has a long-standing tradition as a textbook showpiece of quantum mechanics [1]. A fascinating realization of two-path interference on a macroscopic scale has recently been achieved in near threshold photodetachment microscopy [2][3][4]. Here, electrons are released from negative ions by irradiation with a laser beam in the presence of a uniform external electric field which subsequently governs their motion. Blondel et al. [2][3][4] recorded field-induced interference fringes in configuration space for O − and several other ionic species. In their experiment, the motion of the electrons can be considered as the quantum analogue of throwing a classical particle at constant energy in a uniform gravitational field. Within the classically allowed "shot-put"-range two distinct trajectories will link the electron source with a given destination, causing "double slit" interference in the quantal case. Using detectors with high spatial resolution, images of the resulting fringes were obtained by Blondel et al. [3,4] at large distances (0.5 m) from the electron-emitting negative ions, there extending to the millimeter scale (Fig. 1). In this way, their "photodetachment microscope" demonstrated the nodes and antinodes of the electronic wave function, allowing precise determination of the electron affinity [4]. In order to advance the understanding of the imaging mechanism of their device, this letter serves to point out the intricate spatial properties of the photoelectronic current distribution in parallel electric and magnetic fields. (The integrated photocurrent, i. e. the total photodetachment cross section in parallel fields has been addressed theoretically by several authors [5,6]. Their results are implicitly contained in the following developments.)