Larry, this link helped explain some aspects of multiparticle wave functions to me: http://galileo.phys.virginia.edu/classes/252/symmetry/Symmetry.html. They seem to deal with the full space of x and y positions, with the derivatives defined analytically, and then they impose either symmetric or anti-symmetric conditions on possible solutions depending on whether the particles are bosons or fermions. I'm not sure if this will fully answer your question but perhaps it will shed some light.