On a Domain Characterization of Schrodinger Operators with Gradient Magnetic Vector Potentials and Singular Potentials

Of concern are the minimal and maximal operators on L2(R") associated with the differential expression Te = J2{id/dxJ + qJ{x))2 + W{x) j=i where (q.#„) = gradQ for some real function W on R" and W satisfies ¿M-2 < W(Jf) < C|x|~2 . In particular, for Q = 0, Xq reduces to the singular Schrödinger operator -A+ W{x). Among other results, it is shown that the maximal operator (associated with the xq ) is the closure of the minimal operator, and its domain is precisely Dom [ ^2(id/dXj + qj(x))1 J n Dom(tt'), provided that C > c> -n(n 4)/4 .