Abstract
The three-dimensional Schrodinger operator H with constant magnetic field of strength b> 0 is considered under the assumption that the electric potential V ∈ L 1 (R 3 ) admits certain power-like estimates at infinity. The asymptotic behavior as b →∞ of the spectral shift function ξ(E; H, H0) is studied for the pair of operators (H, H0 )a t the energiesE = Eb + λ, E > 0a ndλ ∈ R being fi xed. Two asymptotic regimes are distinguished. In the first regime, called asymptotics far from the Landau levels ,w e pickE/2 � Z+ and λ ∈ R; then the main term is always of order √ b ,a nd is independent of λ. In the second asymptotic regime, called asymptotics near a Landau level ,w e chooseE =2 q0, q0 ∈ Z+ ,a ndλ � 0; in this case the leading term of the SSF could be of order b or √ b for different λ.
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