  The unique property of Coulomb interaction in strict one-dimensional (1D)
system is revealed that the Coulomb repulsion energy of paired electrons is
divergent. As consequences, electrons in 1D system can not doubly occupy the
same spatial orbital and are completely localized. Numerical simulation by time
dependent Hartree-Fock approximation shows this distinct property. The '0.7
anomaly' in 1D electron gas is fully explained by the property. Its possible
contribution to strongly correlated systems is discussed.
