Abstract
This paper is the continuation of our work with Victor Guillemin (previous paper in this volume); Victor and I proved that the Taylor expansion of the potential at a generic non-degenerate critical point is determined by the semi-classical spectrum of the associated Schrödinger operator near the corresponding critical value. Here I show that, under some genericity assumptions, the potential of the 1D Schroedinger operator is determined by its semi-classical spectrum. Moreover, there is an explicit reconstruction. This paper is strongly related to a paper of David Gurarie (J. Math. Phys. 36:1934–1944 (1995)).
Mathematics Subject Classification (2010): 34E20, 81Q10, 81Q20
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To the memory of our friend, the inspiring mathematician, Hans Duistermaat
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de Verdière, Y.C. (2011). A semi-classical inverse problem II: reconstruction of the potential. In: Kolk, J., van den Ban, E. (eds) Geometric Aspects of Analysis and Mechanics. Progress in Mathematics, vol 292. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8244-6_4
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DOI: https://doi.org/10.1007/978-0-8176-8244-6_4
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