  We study nodes of fermionic ground state wave functions. For 2D and higher we
prove that spin-polarized, noninteracting fermions in a harmonic well have two
nodal cells for arbitrary system size. The result extends to other
noninteracting/mean-field models such as fermions on a sphere, in a periodic
box or in Hartree-Fock atomic states. Spin-unpolarized noninteracting states
have multiple nodal cells, however, interactions and many-body correlations
generally relax the multiple cells to the minimal number of two. With some
conditions, this is proved for interacting 2D and higher dimensions harmonic
fermion systems of arbitrary size using the Bardeen-Cooper-Schrieffer
variational wave function. Implications and extent of these results are briefly
discussed.
