Absolute Continuity of the Spectrum of a Periodic 3D Magnetic Schrödinger Operator with Singular Electric Potential

We prove that the spectrum of a periodic 3D magnetic Schrödinger operator whose electric potential is the derivative of a measure is absolutely continuous provided that the distribution is -bounded in the sense of quadratic forms with bound not exceeding some constant , and the periodic magnetic pot...

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Bibliographic Details
Published in:Mathematical Notes 2021-09, Vol.110 (3-4), p.497-510
Main Author: Danilov, L. I.
Format: Article
Language:English
Subjects:
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Electric potential
Mathematics
Mathematics and Statistics
Operators (mathematics)
Quadratic forms
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Summary:We prove that the spectrum of a periodic 3D magnetic Schrödinger operator whose electric potential is the derivative of a measure is absolutely continuous provided that the distribution is -bounded in the sense of quadratic forms with bound not exceeding some constant , and the periodic magnetic potential satisfies certain conditions, which, in particular, hold if for some or for some .
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434621090200