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)


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):
$$ {\left( {\frac{1}{i}\frac{\partial }{{\partial x}} + A\left( x \right)} \right)^{2}}u + V\left( x \right)u = {k^{2}}u$$
or equivalently
$$ - \Delta u - 2i\sum\limits_{{j = 1}}^{n} {Aj} \left( x \right)\frac{{\partial u}}{{\partial {x_{j}}}} + q\left( x \right)u = {k^{2}}u$$
where We will assume that the potentials A and V are real-valued and exponentially decreasing, i.e.


Inverse Problem Compact Support Schrodinger Equation Magnetic Potential Inverse Scattering Problem 
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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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