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Erschienen in:
2011 | OriginalPaper | Buchkapitel
A semi-classical inverse problem II: reconstruction of the potential
verfasst von : Yves Colin de Verdière
Erschienen in: Geometric Aspects of Analysis and Mechanics
Verlag: Birkhäuser Boston
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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)).