  We test the Salpeter formalism for the electron screening of the solar
proton-proton fusion reaction by solving numerically the relevant Schrodinger
equation. We evaluate exactly the square of the overlap integral of the
two-proton wave function and the deuteron wave function and compare with the
usual analytic approximation. The usual WKB solution agrees with the numerical
result to $O(10^{-4})$. The WKB approximation should be even more precise for
the other nuclear fusion reactions in the $pp$ chain and CNO cycles.
