Geodesic
Spectral Asymptotics for the Schrödinger Operator on the Line with Spreading and Oscillating Potentials
Documenta mathematica, Tome 23 (2018), pp. 599-636
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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.
DOI : 10.4171/dm/627
Classification : 34E10, 34L15, 34L40
Mots-clés : Schrödinger operator, normal form, spectral asymptotics, rapid oscillations, WKB expansion 
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     author = {Vincent Duch\^ene and Nicolas Raymond},
     title = {Spectral {Asymptotics} for the {Schr\"odinger} {Operator} on the {Line} with {Spreading} and {Oscillating} {Potentials}},
     journal = {Documenta mathematica},
     pages = {599--636},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/627},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/627/}
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Vincent Duchêne; Nicolas Raymond. Spectral Asymptotics for the Schrödinger Operator on the Line with Spreading and Oscillating Potentials. Documenta mathematica, Tome 23 (2018), pp. 599-636. doi: 10.4171/dm/627

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