  We derive some rigorous results concerning the backflow operator introduced
by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not
compact. Thus the question is underlined whether the backflow constant is an
eigenvalue of the backflow operator. From the position representation of the
backflow operator we obtain a more efficient method to determine the backflow
constant. Finally, detailed position probability flow properties of a numerical
approximation to the (perhaps improper) wave function of maximal backflow are
displayed.
