Scattering solutions and Born approximation for the magnetic Schr\"odinger operator
Abstract
We prove the existence of scattering solutions for multidimensional magnetic Schr\"odinger equation which belong to the weighted Sobolev space H1s (Rn)(n=2,3) with some s < -1/2. As a consequence of this we formulate the direct Born approximation for the magnetic Schr\"odinger operator. Possible connections with inverse problems (inverse scattering Born approximation) are discussed.
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