SCHRODINGER-OPERATORS WITH MAGNETIC AND ELECTRIC POTENTIALS

In the present paper, we consider Schrodinger operators which are formally given by [GRAPHICS] In Section 2 and 3 we prove that P has a regularly accretive extension which is a self-adjoint extension of P and it is the only self-adjoint realisation of P in L2(R(N)) when a satisfies a = (a1, a2, ..., a(N)) is-an-element-of L(loc)2(R(N))N, a(j) real-valued, 1 less-than-or-equal-to j less-than-or-equal-to N, V is-an-element-of L(loc)1(R(N)), real-valued and the negative part V- := max (0, -V) satisfys integral-R(N) V-\phi\2 dx less-than-or-equal-to C1 parallel-to delphi parallel-to 2 + C2 parallel-to phi parallel-to 2 phi is-an-element-of H1,2(R(N)), with constants 0 less-than-or-equal-to C1 < 1, C2 greater-than-or-equal-to 0 independent of V. In Section 4, we prove that P is essential self-adjoint on C0infinity (R(N)) when a, V satisfy a is-an-element-of L(loc)4 (R(N))N, div a is-an-element-of L(loc)2 (R(N)); V = V1 + V2, V real-valued, V(i) is-an-element-of L(loc)2 (R(N)), i = 1, 2, V1(x) greater-than-or-equal-to -C\x\2, for x is-an-element-of R(N) with C greater-than-or-equal-to 0 and 0 greater-than-or-equal-to V2 is-an-element-of K(N).