A semi-classical inverse problem II: reconstruction of the potential

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dc.creatorde Verdière, Yves Colin
dc.date2008-02-12
dc.date.accessioned2026-07-07T09:20:15Z
dc.date.available2026-07-07T09:20:15Z
dc.descriptionThis paper is the continuation of our work with Victor Guillemin; 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)).
dc.description21 pages 5 Figures
dc.identifierhttps://arxiv.org/abs/0802.1643
dc.identifierhttp://arxiv.org/abs/0802.1643
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154664
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectSpectral Theory
dc.subject34E20, 81Q10, 81Q20
dc.titleA semi-classical inverse problem II: reconstruction of the potential
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