  High-frequency solutions of one or several Schr\"odinger-type equations are
well known to differ very little from the plane wave solutions $\exp[\pm ik
x]$. That is, the potential terms impact the envelope of a high-frequency plane
wave by only a small amount. However, when such equations are solved by a
finite-difference method, the highest-frequency solutions may, under certain
conditions, turn out to be localized. In this letter we explain this numerical
artifact.
