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Schr\"{o}dinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum

Stanislav A. Molchanov·Boris R. Vainberg
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Abstract

It is proven that the absolutely continuous spectrum of matrix Schr\"{o}dinger 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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Stanislav A. Molchanov, Boris R. Vainberg. 2003-08-09. Schr\"{o}dinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum. https://arxiv.org/abs/math-ph/0308012

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