  Starting from the Abrikosov-Ryzhkin formulation of the 1D random potential
problem I find closed functional representations for various physical
quantities. These functional integrals are calculated exactly without the use
of any perturbative expansions. The expressions for the multipoint densities
correlators are obtained. Then I evaluate the mean square dispersion of the
size of localized wave functions. As a physical application of the method, I
find the expectation value of the persistent current in mesoscopic ring with
arbitrary magnetic flux $\Phi$. (For small $\Phi$ this problem has been solved
by O.Dorokhov). The case when the random potential has finite correlation
length is considered too.
