Eskin, G. Inverse spectral problem for the Schrödinger equation with periodic vector potential. (English) Zbl 0697.35168 Commun. Math. Phys. 125, No. 2, 263-300 (1989). The author considers the Schrödinger equation \[ H\Psi =\lambda \Psi \quad or\quad (i(\partial /\partial x_ 1)+A_ 1(x))^ 2\Psi +(i(\partial /\partial x_ 2)+A_ 2(x))^ 2\Psi +V(x)\Psi (x)=\lambda \Psi (x), \] with \(\bar A(x)=(A_ 1(x),A_ 2(x))\) is the vector potential, and V(x) is the scalar potential. \(H_ 0\) is the periodic spectrum of H, \(H_ r\) is the Floquet spectrum of H, and B is the curl of \(\bar A.\) He studies the inverse spectrum problem of recovering B(x) and V(x) from \(H_ 0\) or \(H_ r\). Reviewer: H.S.Nur Cited in 10 Documents MSC: 35R30 Inverse problems for PDEs 35P05 General topics in linear spectral theory for PDEs 35J10 Schrödinger operator, Schrödinger equation Keywords:periodic spectrum; Floquet spectrum PDFBibTeX XMLCite \textit{G. Eskin}, Commun. Math. Phys. 125, No. 2, 263--300 (1989; Zbl 0697.35168) Full Text: DOI References: [1] Ashcroft, N., Mermin, N. D.: Solid state physics. Philadelphia, PA,: Holt, Rinehart and Winston 1976 · Zbl 1107.82300 [2] Courant, R., Hilbert, D.: Methods of mathematical physics, vol. II. New York, London: Academic Press 1962 · Zbl 0099.29504 [3] Eskin, G., Ralston, J., Trubowitz, E.: On isospectral periodic potentials inR n. Commun. Pure Appl. Math.37, 647-676 (1984) · Zbl 0574.35021 · doi:10.1002/cpa.3160370505 [4] Eskin, G., Ralston, J., Trubowitz, E.: On isospectral periodic potentials inR n, II. Commun. Pure Appl. Math.37, 715-753 (1984) · Zbl 0582.35031 · doi:10.1002/cpa.3160370602 [5] Guillemin, V., Uribe, A.: Clustering theorems with twisted spectra. Math. Ann.2731, 479-506 (1986) · Zbl 0591.58031 · doi:10.1007/BF01450735 [6] Maslov, V. P., Fedoriuk, M. V.: Semi-classical approximation in quantum mechanics. Dordrecht: D. Reidel 1981 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.