Spectral theory of magnetic Schrödinger operators with exploding potentials (Q809330)

Denote by H the (unique) selfadjoint extension of the Schrödinger operator \[ L=-\sum^{n}_{j=1}(\frac{\partial}{\partial x_ j}+ib_ j(x))^ 2+V(x), \] defined on \(C^{\infty}_ 0({\mathbb{R}}^ n)\), where the potential V is supposed to satisfy V(x)\(\to -\infty\) (\(| x| \to \infty)\) and \(V(x)\geq -C| x|^{\alpha}\) (\(| x| \geq R)\) for some \(\alpha <2\). The author studies conditions for the absolute continuity of H and derives its spectral representation. This continues previous work of Ikebe, Kato, Uchiyama, Eastham and Kalf.