A semi-classical inverse problem I: Taylor expansions.

Yves Colin de Verdière (1) , Victor Guillemin (2)

1 IF - Institut Fourier
2 Math. Dep.

In dimension 1, we show that the Taylor expansion of a potential near a generic non degenerate critical point can be recovered from the knowledge of the semi-classical spectrum of the associated Schrödinger operator near the corresponding critical value.

Mots clés: Schrödinger operator; semi-classics; inverse spectral problem; trace formulae; Birkhoff normal form

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Yves Colin de Verdière, Victor Guillemin. A semi-classical inverse problem I: Taylor expansions.. 2008. ⟨hal-00250568⟩