Schrödinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum

Details Schrödinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum Schrödinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum

2003-08-09

arxiv.org/abs/math-ph/0308012v1

Physics

Mathematical Physics

Scientific paper

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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