  We study the internal rotational dynamics of electronic beams in relation to
the phase singularities of their wave functions. Given their complex
singularity structure, Hermite-Gaussian beams and other superpositions of
Laguerre-Gaussian modes are studied here. We show that by inspecting the lowest
non-vanishing terms of the wave function near the singularity it is possible to
infer the structure of the Bohmian streamlines. Conversely, starting from a map
of the electron's Bohmian velocities, we demonstrate that it is possible to
derive the form of the electron's wave function near the singularity. We
outline a procedure that could yield an experimental method to determine the
main parameters of the electron's wave function close to a singularity.
