Asymptotic of the density of states for the Schr{umlt o}dinger operator with periodic electromagnetic potential

Journal Article · Fri Aug 01 00:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532105· OSTI ID:526894

Mohamed, A ^[1]

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1. CNRS UMR 6629, Department de Mathematiques, Universite de Nantes, 2, rue de la Houssiniere, BP 92208 F-44322 Nantes Cedex 3 (France)

For the Schr{umlt o}dinger operator in L{sup 2}({bold R}{sup n}), n{gt}1, with C{sup {infinity}} periodic electromagnetic potential, we give an asymptotic formula of the integrate density of states of the form N({mu})=a{sub n}{mu}{sup n/2}+{bold O}({mu}{sup (n{minus}2+{epsilon})/2}), {forall}{epsilon}{gt}0. When n=2, this estimate enables us to prove the finiteness of gaps in the spectrum. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 526894
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DENSITY
ELECTRIC POTENTIAL
GAUGE INVARIANCE
MAGNETIC FIELDS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
SCHROEDINGER PICTURE
SPECTRA