Abstract
There exist several sum rules and rigorous theorems for a jellium surface, which can be derived as special cases of the general theorems valid for many-body systems. These theorems provide a link between the bulk and surface quantities and may be used to test the internal consistency of calculation of surface properties. This chapter presents some of these relations based on the charge neutrality of the system, the Hellmann–Feynman theorem, and the virial theorem. Hellmann–Feynman theorem has been applied successfully to the calculations for the many-body systems because of its basic simplicity. . The chapter explains that among many applications, a special case of this theorem, the electrostatic theorem, has been proved to be useful in surface physics problems.
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