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It is demonstrated that non‐locality and non‐linearity of Hartree‐Fock equations dramatically affect the properties of their solutions that essentially differ from solutions of Schrödinger equation with a local potential. Namely, it acquires extra zeroes, has different coordinate asymptotic, violates so‐called gauge‐invariance, has different scattering phases at zero energy, has in some cases several solutions with the same set of quantum numbers, usually equivalent expressions of current and Green's functions became non‐equivalent. These features result in a number of consequences for probabilities of some physical processes, leading e. g. to extra width of atomic Giant resonances and enhance considerably the ionization probability of inner atomic electrons by a strong field (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Big Consequences of Small Changes (Non‐locality and non‐linearity of Hartree‐Fock equations)