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New approach to quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field

journal contribution
posted on 2023-06-08, 15:52 authored by Michael MelgaardMichael Melgaard
For a 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. 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 E 0. In particular it is shown that E 0 can be an eigenvalue of H m . Furthermore, asymptotic expansions of the scattering matrix associated with the pair (H m , H om ) are derived as the energy parameter tends to E 0.

History

Publication status

  • Published

Journal

Few-Body Systems

ISSN

0177-7963

Publisher

Springer Verlag

Issue

1-2

Volume

32

Page range

1-22

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-09-19

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