Vortices in Atomic Processes
Pp. 3-28 (26)
Joseph H. Macek
The time-dependent Schrödinger equation describes dynamical processes of one-electron
species in terms of complex wave functions. The functions are inherently complex; therefore zeros
occur only when both the real and imaginary parts of the wave functions vanish. If this happens at
isolated points rather than on nodal surfaces one can show that the zeros must correspond to vortices.
An imaging theorem is given which shows how such vortices can be seen experimentally. Since the
theorem requires time propagation from microscopic to macroscopic scales, a method is developed that
does just the same. Examples of vortices that emerge in dynamical processes are given. The vortices
that we find are linked to the hydrodynamic interpretation of Schrödinger's time-dependent equation.
Department of Physics and Astronomy, University of Tennessee and Oak Ridge, National Laboratory, TN 37996-1501 Knoxville, USA.