Schrödinger operators with magnetic and electric potentials

In the present paper, we consider Schrödinger operators which are formally given by . 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 (RN) when satisfies = (a1, a2, …, aN) ∈ , aj, real-valued, , real-valued and the negative part V-:= max(0, -V) satisfys , with constants 0 ≤ C1 < 1, C2 ≥ 0 independent of V. In Section 4, we prove that P is essential self-adjoint on when , V sat0isfy ; V = V1 + V2, V real-valued, , i = 1, 2, V1(x) ≥ –C |x|2, for x ∈ RN with C ≥ 0 and 0 ≥ V2 ∈ KN.