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Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field

journal contribution
posted on 2023-06-08, 15:51 authored by Michael MelgaardMichael Melgaard
For fixed magnetic quantum number $m$ results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential $V$. In various, mostly fairly singular settings asymptotic expansions for the resolvent of the Hamiltonian $H_{m}=H_{om}+V$ are deduced as the spectral parameter tends to the lowest Landau threshold. Furthermore, scattering theory for the pair $(H_{m}, H_{om})$ is established and asymptotic expansions of the scattering matrix are derived as the energy parameter tends to the lowest Landau threshold

History

Publication status

  • Published

Journal

Central European Journal of Mathematics

ISSN

1895-1074

Publisher

Central European Science Journals

Issue

4

Volume

1

Page range

477-509

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-09-19

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