  I propose to use Hamiltonians which contain two-dimensional and
three-dimensional kinetic terms for the description of two-dimensional systems
in physics.
  As a model system the evolution of three-dimensional wavefunctions in the
presence of an infinitely thin layer is studied. The model predicts distance
laws for correlation functions which interpolate between two-dimensional and
three-dimensional behavior. It also predicts that in certain cases transmission
probabilities through thin layers should depend not only on the transverse, but
also on the longitudinal momentum of the infalling particles.
  The model also yields a static potential which interpolates between the
two-dimensional logarithmic potential at small distances and the
three-dimensional (1/r)-potential at large distances.
