  In orbital-free density functional theory (OFDFT), an equation exists for
$\psi = \sqrt n$, the square root of the ground state electron density $n$. We
show that $\psi$ cannot be expanded as a linear combination of elements of a
complete set of basis functions except in the case of one or two electron
systems. This is unlike the case for the ground state of a system of identical
bosons in which the square root of the ground state bosonic density can have an
expansion as a linear combination of elements of a complete set of basis
functions.
