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

The impossibility of expanding the square root of the electron density as a linear combination of elements of a complete set of basis functions