CONVERGENCE OF NELSON DIFFUSIONS WITH TIME-DEPENDENT ELECTROMAGNETIC POTENTIALS

Some recent results on the convergence of Nelson diffusions are extend ed to the case of Schrodinger operators with time-dependent electromag netic potentials. It is proven that the sequence {P(n)}n greater-than- or-equal-to 1 of measures on the canonical space of physical trajector ies associated to the solutions of Schrodinger equations in Nelson's s cheme, corresponding to the sequence {(V(n),A(n))}n greater-than-or-eq ual-to 1 subset-of C1(R;R X L2(R3)), converges in the total variation norm under the assumptions that for every fixed t the scalar potential s V(n)(t) converge in R, the space of Rollnik class potentials, and th e vector potentials A(n)(t) converge in L(loc)infinity(R;L2(R3)). In o rder to prove these results conditions are given under which solutions of Schrodinger equations are continuous in the (time-dependent electr omagnetic) potentials in the norm of the Sobolev space H-1(R3).