  In a two-dimensional approximation, the probability density and current for a
photoelectron near the localization of a quantum vortex are theoretically
investigated. The wave function in the momentum representation, which we found
earlier, is simplified near zero, corresponding to the center of the vortex.
This allows us to obtain a simple analytical expression for it, which has the
structure of a Gaussian wave packet and contains basic information about the
vortex. It is used to analyze the temporal evolution of a quantum vortex, both
in momentum and coordinate space. The effect of the intensity of an ionizing
ultrashort laser pulse on the shape of a quantum vortex is also investigated.
