Quantization of a toy model of a pseudointegrable Hamiltonian impact system
is introduced, including EBK quantization conditions, a verification of Weyl’s
law, the study of their wavefunctions and a study of their energy levels
properties. It is demonstrated that the energy levels statistics are similar to
those of pseudointegrable billiards. Yet, here, the density of wavefunctions
which concentrate on projections of classical level sets to the configuration
space does not disappear at large energies, suggesting that there is no
equidistribution in the configuration space in the large energy limit; this is
shown analytically for some limit symmetric cases and is demonstrated
numerically for some nonsymmetric cases.
