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.

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