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arXiv · 0802.1643

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

Yves Colin de Verdière
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Abstract

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 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)).

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Yves Colin de Verdière. 2008-02-12. A semi-classical inverse problem II: reconstruction of the potential. https://arxiv.org/abs/0802.1643

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