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Inverse Scattering Problems For Schrödinger Operators with Magnetic and Electric Potentials

  • G. Eskin
  • J. Ralston
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 90)

Abstract

Consider the Schrödinger equation in R n , n ≥ 3, with magnetic potential A(x) = (A 1(x),…,A n (x)) and electric potential V(x):
$$ {\left( {\frac{1}{i}\frac{\partial }{{\partial x}} + A\left( x \right)} \right)^{2}}u + V\left( x \right)u = {k^{2}}u$$
(1.1)
or equivalently
$$ - \Delta u - 2i\sum\limits_{{j = 1}}^{n} {Aj} \left( x \right)\frac{{\partial u}}{{\partial {x_{j}}}} + q\left( x \right)u = {k^{2}}u$$
(1.2)
where We will assume that the potentials A and V are real-valued and exponentially decreasing, i.e.

Keywords

Inverse Problem Compact Support Schrodinger Equation Magnetic Potential Inverse Scattering Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • G. Eskin
    • 1
  • J. Ralston
    • 1
  1. 1.Department of MathematicsUCLALos AngelesUSA

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