 
Summary: SemiClassicalFourierIntegralOperatorValued Pseudodifferential
Operators and Scattering in a Strong Magnetic Field
Ivana Alexandrova
1400 Washington Avenue, Earth Sciences 110, Department of Mathematics and Statistics,
State University of New York, Albany, NY 12222, 5184374489, ialexandrova@albany.edu
Abstract
We study the microlocal structure of the semiclassical scattering amplitude for
Schršodinger operators with a strong magnetic and a strong electric fields at non
trapping energies. We prove that the leading term of the scattering amplitude can
be approximated by a semiclassicalFourierintegraloperatorvalued pseudodifferen
tial operator.
1 Introduction
We consider the scattering amplitude for a Schršodinger operator with a strong magnetic
and a strong electric fields and we prove that the leading term of the scattering amplitude
can be approximated by a semiclassicalFourierintegraloperatorvalued pseudodifferential
operator.
For n 3 and b > 0 let H(b) = H0(b) + bV, where the electric potential V satisfies
V = V (x, y, z) = V
(z) + W (x, y, z), W C
c (Rn
