Abstract
By considering the behaviour as N → ∞ of the ratio of L 2[0, N] norms of solutions of −d 2 dr 2 + 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 = −d 2 dr 2 + V(r) is regular at 0 and in the limit point case at infinity, with V( r) locally integrable.
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