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

Open Mathematics (2003)

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

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topMichael 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 -

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