Résurgence de Voros et périodes des courbes hyperelliptiques
Résumé
The aim of this article is to formulate in a geometrical way the master idea of Voros [ in Ann. Inst. Henri Poincaré, Sect. A 39, 211-238 (1983) ] : the solutions of the one dimensional stationary Schrödinger equation with a polynomial potential are exactly encoded in the complex domain by their WKB expansions (formal divergent expansions in powers of Planck’s constant) in a way which can be read in the geometry of periods of the differential form p d q ( q = position variable, ( p =classicial momentum).