Colin de Verdière, Yves; Guillemin, Victor A semi-classical inverse problem. I: Taylor expansions. (English) Zbl 1258.34036 van den Ban, Erik P. (ed.) et al., Geometric aspects of analysis and mechanics. In honor of the 65th birthday of Hans Duistermaat. Basel: Birkhäuser (ISBN 978-0-8176-8243-9/hbk; 978-0-8176-8244-6/ebook). Progress in Mathematics 292, 81-95 (2011). The authors show that the Taylor expansion of a “generic” potential near a nondegenerate critical point can be recovered from the knowledge of the semi-classical spectrum of the associated Schrödinger operator near the corresponding critical value. In contrast to previous works, in this paper the authors do not assume that the potential is even.For the entire collection see [Zbl 1218.00014]. Reviewer: Alexey Fedoseev (Saratov) Cited in 1 ReviewCited in 12 Documents MSC: 34A55 Inverse problems involving ordinary differential equations 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 47G30 Pseudodifferential operators Keywords:Schrödinger operator; semi-classics; inverse spectral problem PDFBibTeX XMLCite \textit{Y. Colin de Verdière} and \textit{V. Guillemin}, Prog. Math. 292, 81--95 (2011; Zbl 1258.34036) Full Text: DOI arXiv