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

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

2008-02-12

arxiv.org/abs/0802.1643v1

Physics

Mathematical Physics

21 pages 5 Figures

Scientific paper

This 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 Schr\"odinger 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)).

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