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

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Melgaard M.

Open Mathematics

2003

tom 1

nr 4

477-509

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.

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1 Open Mathematics

1 Melgaard M.

1 2003

Wyniki wyszukiwania

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