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We develop a quantum theory of electron confinement in metal nanofilms. Thetheory is used to compute the nonlinear response of the film to a static orlow-frequency external electric field and to investigate the role of boundaryconditions imposed on the metal surface. We find that the sign and magnitude ofthe nonlinear polarizability depends dramatically on the type of boundarycondition used.

Quantum theory of electric polarization nonlinearity in metal nanofilms