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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 1, Issue 4


Volume 13 (2015)

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

Michael Melgaard
Published Online: 2003-12-01 | DOI: https://doi.org/10.2478/BF02475180


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 singular settings, asymptotic expansions for the resolvent of the Hamiltonian H m+Hom+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.

Keywords: Near-threshold resolvent expansions; scattering matrix; auxiliary one-dimensional Schrödinger operator

Keywords: 47N20; 35J10 35P25 47F05 81U05

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About the article

Published Online: 2003-12-01

Published in Print: 2003-12-01

Citation Information: Open Mathematics, Volume 1, Issue 4, Pages 477–509, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02475180.

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