Duchêne, Vincent; Raymond, Nicolas

Spectral Asymptotics for the Schrödinger Operator on the Line with Spreading and Oscillating Potentials

Doc. Math. 23, 599-636 (2018)
DOI: 10.25537/dm.2018v23.599-636


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.

Mathematics Subject Classification

34L15, 34L40, 34E10


Schrödinger operator, rapid oscillations, spectral asymptotics, normal form, WKB expansion


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Duchêne, Vincent
Univ. de Rennes 1, CNRS, IRMAR-UMR6625, F-35000 Rennes, France
Raymond, Nicolas
Univ. de Rennes 1, CNRS, IRMAR-UMR6625, F-35000 Rennes, France