  The excitation of semiconductor quantum dots often involves an attached
wetting layer with delocalized single-particle energy eigenstates. These
wetting-layer states are usually approximated by (orthogonalized) plane waves.
We show that this approach is too crude. Even for a simple model based on the
effective-mass approximation and containing one or a few lens-shaped quantum
dots in a rectangular wetting layer, the wetting-layer states typically show a
substantially irregular and complex morphology. To quantify this complexity we
use concepts from the field of quantum chaos such as spectral analysis of
energy levels, amplitude distributions, and localization of energy eigenstates.
