Geodesic
Spectral Asymptotics for the Schrödinger Operator on the Line with Spreading and Oscillating Potentials
Documenta mathematica, Tome 23 (2018), pp. 599-636.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

This study is devoted to the asymptotic spectral analysis of multiscale Schrödinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal form filtrating most of the oscillations, a reduction to a non-oscillating effective Hamiltonian is performed.
Classification : 34L15, 34L40, 34E10
Keywords: Schrödinger operator, rapid oscillations, spectral asymptotics, normal form, WKB expansion 
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     author = {Duch\^ene, Vincent and Raymond, Nicolas},
     title = {Spectral {Asymptotics} for the {Schr\"odinger} {Operator} on the {Line} with {Spreading} and {Oscillating} {Potentials}},
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Duchêne, Vincent; Raymond, Nicolas. Spectral Asymptotics for the Schrödinger Operator on the Line with Spreading and Oscillating Potentials. Documenta mathematica, Tome 23 (2018), pp. 599-636. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a45/