Eskin, G.; Ralston, J. Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy. (English) Zbl 0843.35133 Commun. Math. Phys. 173, No. 1, 199-224 (1995). Authors’ abstract: “We consider the Schrödinger operator in \(\mathbb{R}^n\), \(n\geq 3\), with electric and magnetic potentials which decay exponentially as \(|x|\to \infty\). We show that the scattering amplitude at fixed positive energy determines the electric potential and the magnetic field”. Reviewer: Dang Dinh Ang (Ho Chi Minh City) Cited in 4 ReviewsCited in 53 Documents MSC: 35R30 Inverse problems for PDEs 81U40 Inverse scattering problems in quantum theory 35P25 Scattering theory for PDEs Keywords:Schrödinger operator; scattering amplitude; electric potential; magnetic field PDFBibTeX XMLCite \textit{G. Eskin} and \textit{J. Ralston}, Commun. Math. Phys. 173, No. 1, 199--224 (1995; Zbl 0843.35133) Full Text: DOI References: [1] Agmon, S.: Spectral properties of Schrödinger operators and scattering theory. Annali di Pisa, Serie IV,2, 151–218 (1975) · Zbl 0315.47007 [2] Eskin, G., Ralston, J.: The Inverse Backscattering Problem in Three Dimensions. Commun. Math. Phys.124, 169–215 (1989) · Zbl 0706.35136 [3] Faddeev, L.D.: The inverse problem of quantum scattering II. J. Sov. Math.5, 334–396 (1976) · Zbl 0373.35014 [4] Hörmander, L.: Uniqueness theorems for second order elliptic differential equations. Comm. in PDE8, 21–64 (1983) · Zbl 0546.35023 [5] Nakamura, G., Sun, Z., Uhlmann, G.: Global Identifiability for an Inverse Problem for the Schrödinger Equation in a Magnetic Field. Preprint · Zbl 0843.35134 [6] Novikov, R.G., Khenkin, G.M.: The \(\bar \partial \) in the multidimensional inverse scattering problem. Russ. Math. Surv.42, 109–180 (1987) · Zbl 0674.35085 [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 [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 [9] Sun, Z.: An inverse boundary value problem for Schrödinger operator with vector potentials. Trans of AMS338 (2), 953–969 (1993) · Zbl 0795.35143 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.