| Abstrakt: |
We consider the Schrödinger operator H = (I▿ + A)[SUP2] + V in the space L[SUB2](&scriptR;[SUPd]) with long-range electrostatic V(x) and magnetic A(x) potentials. Using the scheme of smooth perturbations, we give an elementary proof of the existence and completeness of modified wave operators for the pair H[SUB0] = - Δ, H. Our main goal is to study spectral properties of the corresponding scattering matrix S(&lembda;). We obtain its stationary representation and show that its singular part (up to compact terms) is a pseudodifferential operator with an oscillating amplitude which is an explicit function of V and A. Finally, we deduce from this result that, in general, for each &lembda; > 0 the spectrum of S(&lembda;) covers the whole unit circle. [ABSTRACT FROM AUTHOR] |
