  A way is presented to design quantum wave functions that exhibit backflow,
namely negative probability current despite having a strictly positive spectrum
of momentum. These wave functions are derived from rational complex functions
which are analytic in the upper half-plane and have zeros in the lower
half-plane through which the backflowing behavior is controlled. In analogy,
backflowing periodic wave functions are derived from rational complex functions
which are analytic in the interior and have appropriately placed zeros or poles
in the exterior of the unit circle. The concept is combined with a Pad\'e-type
procedure to design wave functions of this type that approximate a desired
profile along the interval of backflow.
