Schrödinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum |
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Authors: | S Molchanov |
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Affiliation: | Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA |
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Abstract: | It is proven that the absolutely continuous spectrum of matrix Schrödinger operators coincides (with the multiplicity taken into account) with the spectrum of the unperturbed operator if the (matrix) potential is square integrable. The same result is also proven for some classes of slower decaying potentials if they are smooth. |
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Keywords: | Schrö dinger operator Absolutely continuous spectrum L2-conjecture |
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