  The Aharonov-Bohm effect is the prime example of a zero-field-strength
configuration where a non-trivial vector potential acquires physical
significance, a typical quantum mechanical effect. We consider an extension of
the traditional A-B problem, by studying a two-dimensional medium filled with
many point-like vortices. Systems like this might be present within a Type II
superconducting layer in the presence of a strong magnetic field perpendicular
to the layer, and have been studied in different limits. We construct an
explicit solution for the wave function of a scalar particle moving within one
such layer when the vortices occupy the sites of a square lattice and have all
the same strength, equal to half of the flux quantum. From this construction we
infer some general characteristics of the spectrum, including the conclusion
that such a flux array produces a repulsive barrier to an incident low-energy
charged particle, so that the penetration probability decays exponentially with
distance from the edge.
