On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators

AbstractBy considering the behaviour as N → ∞ of the ratio of L2[0, N] norms of solutions of −d2dr2 + V(r)u= xu, 0 ⩾r⩽∞, x∈R a characterisation of the absolutely continuous and singular spectra of one-dimensional Schrödinger operators is deduced. The analysis is applicable to all operators for which L = −d2dr2 + V(r) is regular at 0 and in the limit point case at infinity, with V(r) locally integrable