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

Michael Melgaard

Open Mathematics (2003)

  • Volume: 1, Issue: 4, page 477-509
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Michael Melgaard. "Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field." Open Mathematics 1.4 (2003): 477-509. <http://eudml.org/doc/268892>.

@article{MichaelMelgaard2003,
abstract = {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.},
author = {Michael Melgaard},
journal = {Open Mathematics},
keywords = {47N20; 35J10 35P25 47F05 81U05},
language = {eng},
number = {4},
pages = {477-509},
title = {Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field},
url = {http://eudml.org/doc/268892},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Michael Melgaard
TI - Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field
JO - Open Mathematics
PY - 2003
VL - 1
IS - 4
SP - 477
EP - 509
AB - 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.
LA - eng
KW - 47N20; 35J10 35P25 47F05 81U05
UR - http://eudml.org/doc/268892
ER -

References

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