Equivalence of the Plasmon Energy and the Surface Energy Barrier in Simple Metals

Kohn’s theorem demonstrates duality (or equivalence) of the plasmonic and single-particle responses of simple metals in the long wavelength limit. It is shown here, that this duality implies, surprisingly, that the surface energy barrier, which confines electrons inside the metal is equal to the plasmon energy. In addition to being of fundamental importance, this remarkable quantum-plasmonic result proves also an old and closed formula, which predicts the electron work function of various metals better than the best “ab-initio” simulations.