  We investigate localization of low-energy modes of the Laplacian with a point
scatterer on a rectangular plate. We observe that the point scatterer acts as a
barrier confining the low-level modes to one side of the plate while assuming
the Dirichlet boundary condition at a point does not induce this type of
localization. This low-energy phenomenon extends to higher modes as we increase
the eccentricity of the plate.
