(1) School of Mathematical Science, Seoul National University, Seoul 151-747, Korea;(2) Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA
Abstract:
We prove in two dimensions that the set of Cauchy data for the Pauli Hamiltonian
measured on the boundary of a bounded open subset with smooth enough boundary determines
uniquely the magnetic field and the electrical potential provided that the electrical potential is
small in an appropriate topology. This result has the immediate consequence, in the case that the
magnetic potential and electrical potential have compact support, that we can determine uniquely
the magnetic field and the electrical potential by measuring the scattering amplitude at a fixed
energy provided that the electrical potential is small in an appropriate topology.