Semiclassical Sum Rules

The expression vertical-barPsi/sub n/(0) vertical-bar/sup 2/ = (2..mu..)/sup 3/2/E/sub n//sup 1/2/(dE/sub n//dn)/4..pi../sup 2/, relating the square of the nth s-wave wave function at the origin to the bound-state reduced mass ..mu.. and the excitation energy E/sub n/, is derived semiclassically. The relation is then used to obtain several sum rules for electron-positron annihilation and an expression for the contribution of a given flavor of heavy quark to the photon-nucleon total cross section.