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It is demonstrated that the collective and single particle responses ofsimple metals in the extreme long wavelength limit become identical. Whenapplied to alternative models of a metallic slab, this duality provesequivalence of the plasma frequency and the surface energy barrier, whichconfines electrons inside the metal. This in-turn proves also a simple, yetpowerful formula, which expresses the work function of a metals as a differencebetween its free-electron plasmon and Fermi energies, and which has been shownto be more accurate (even for complex metals) than the best availablesimulations.

Duality of the collective and single particle responses in simple metals in the extreme long wavelength limit