  It is well-known that a delta potential well in 1D has only one bound state
but that in 3D it supports an {\it infinite} number of bound states with {\it
infinite} binding energy for the lowest level. We show how this also holds for
the less familiar 2D case, and then discuss why this makes 3D delta potential
wells unphysical as models of interparticle interactions for condensed-matter
many-body systems. However, both 2D and 3D delta wells can be ``regularized''
to support a single bound level which in turn renders them conveniently simple
single-parameter interactions, e.g., for modeling the pair-forming dynamics of
quasi-2D superconductors such as the cuprates, or in 3D of other
superconductors and of neutral-fermion superfluids such as ultra-cold trapped
Fermi gases.
