  The role of electronic interactions in the level structure of semiconductor
quantum dots is analyzed in terms of the correspondence to the integrability of
a classical system that models these structures. We find that an otherwise
simple system is made strongly non-integrable in the classical regime by the
introduction of particle interactions. In particular we present a two-particle
classical system contained in a $d$-dimensional billiard with hard walls.
Similarly, a corresponding two-dimensional quantum dot problem with three
particles is shown to have interesting spectral properties as function of the
interaction strength and applied magnetic fields.
