Decay properties of spatial molecular orbitals

Using properties of the Fourier transform we prove that if a Hartree–Fock molecular spatial orbital is in $L_1\left(R^3\right)$, then it decays to zero as its argument diverges to infinity. The proof is rigorous, elementary and short. Our result implies that occupied orbitals with positive eigenvalues will decay to zero provided they are in $L_1$.