Résurgence de Voros et périodes des courbes hyperelliptiques

Dillinger, H.; Delabaere, E.; Pham, Frédéric

doi:10.5802/aif.1326

Dillinger, H. ; Delabaere, E. ; Pham, Frédéric

Annales de l'Institut Fourier, Tome 43 (1993) no. 1, pp. 163-199.

Résumé
Abstract

Le but de cet article est de formuler de façon géométrique l’idée maîtresse de Voros $[$ dans Ann. Inst. Henri Poincaré, Sect. A 39, 211-238 (1983) $]$ : les solutions de l’équation de Schrödinger stationnaire à une dimension, à potentiel polynomial, sont codées exactement dans le domaine complexe par leurs développements BKW (développements formels, divergents, en puissances de la constante de Planck), d’une façon entièrement lisible dans la géométrie des périodes de la forme $p d q$ ( $q$ =variable de position, $p$ = impulsion classique).

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).

EuDML MR Zbl | 10 citations dans Numdam

DOI : 10.5802/aif.1326

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     journal = {Annales de l'Institut Fourier},
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Dillinger, H.; Delabaere, E.; Pham, Frédéric. Résurgence de Voros et périodes des courbes hyperelliptiques. Annales de l'Institut Fourier, Tome 43 (1993) no. 1, pp. 163-199. doi : 10.5802/aif.1326. https://www.numdam.org/articles/10.5802/aif.1326/

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