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

Melgaard, Michael (2002) New approach to quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field. Few-Body Systems, 32 (1-2). pp. 1-22. ISSN 0177-7963

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Michael Melgaard
Date Deposited: 19 Sep 2013 13:25
Last Modified: 19 Sep 2013 13:25
URI: http://sro.sussex.ac.uk/id/eprint/46392
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