The integrated density of stated of one-dimensional random Schrodinger operator with white noise potential and background

Abstract

IX - _(10) tp' (0) sin IX = 0, rJ.,p tp(l) cos P - ptl} tp' (I) sin p = 0, where (B(t))t~O is the standard Brownian motion and B'(t) is the derivative of its sample function, namely the white noise. (p(t))t~O' (q(t))t;a>:o and (r(t))t:<!:o are bounded semi-martingales which we shall call the background, and c is a coupling constant.