Spectral theory of one-dimensional Schrödinger operators with strongly fluctuating potentials (Q1178120)

The authors consider the Schrödinger operator \(-d^2/dx^2+V(x)\), with unbounded potentials, which do not satisfy the criteria of \textit{A. Molchanov} [Tr. Mosk. Mat. O-va. 2, 169--199 (1953; Zbl 0052.10201)]. Of special interest in this presentation are the cases, in which fluctuations of \(V(x)\) may increase without limit and may change in sign, even it may be negative. The investigation is limited to simple models, with piecewise constant potentials, may be with random distributions of width and amplitudes.