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