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Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy. (English) Zbl 0843.35133
Authors’ abstract: “We consider the Schrödinger operator in n , n3, with electric and magnetic potentials which decay exponentially as |x|. We show that the scattering amplitude at fixed positive energy determines the electric potential and the magnetic field”.

MSC:
35R30Inverse problems for PDE
81U40Inverse scattering problems (quantum theory)
35P25Scattering theory (PDE)
References:
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[3]Faddeev, L.D.: The inverse problem of quantum scattering II. J. Sov. Math.5, 334–396 (1976) · Zbl 0373.35014 · doi:10.1007/BF01083780
[4]Hörmander, L.: Uniqueness theorems for second order elliptic differential equations. Comm. in PDE8, 21–64 (1983) · Zbl 0546.35023 · doi:10.1080/03605308308820262
[5]Nakamura, G., Sun, Z., Uhlmann, G.: Global Identifiability for an Inverse Problem for the Schrödinger Equation in a Magnetic Field. Preprint
[6]Novikov, R.G., Khenkin, G.M.: The ¯ in the multidimensional inverse scattering problem. Russ. Math. Surv.42, 109–180 (1987) · Zbl 0674.35085 · doi:10.1070/RM1987v042n03ABEH001419
[7]Novikov, R.G.: The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator. J. Funct. Anal.103, 409–463 (1992) · Zbl 0762.35077 · doi:10.1016/0022-1236(92)90127-5
[8]Novikov, R.G.: The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential. Commun. Math. Phys.161, 569–595 (1994) · Zbl 0803.35166 · doi:10.1007/BF02101933
[9]Sun, Z.: An inverse boundary value problem for Schrödinger operator with vector potentials. Trans of AMS338 (2), 953–969 (1993) · Zbl 0795.35143 · doi:10.2307/2154438