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Quantum scattering theory for long and short range perturbations of the magnetic field. (Théorie de la diffusion quantique pour des perturbations à longue et courte portée du champ magnétique.) (French) Zbl 0780.35091

Summary: The authors study perturbations of the positive Laplace operator, \(- \Delta\), in \(\mathbb{R}^ n\) of the form: \[ H_{A,V}= \sum(D_ j-A_ j(x))^ 2+V(x). \] In case when \(V\) is short range, \(A(x)=\sum A_ j(x)dx_ j\) long range but the two form \(dA\) being short range, they compare the usual Moeller wave operators and the modified wave operators introduced by Isozaki-Kitada. They recover a result of Loss-Thaller on the completeness of the wave operators for the pair \((H_{A,V},- \Delta)\).

MSC:

35Q40 PDEs in connection with quantum mechanics
35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
81U05 \(2\)-body potential quantum scattering theory
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