Abstract
Abstract
We derive a system of TBA equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and they can be regarded as the solution of a Riemann-Hilbert problem in resurgent Quantum Mechanics formulated by Voros. Our derivation builds upon the solution of similar Riemann-Hilbert problems in the study of BPS spectra in
$$ \mathcal{N} $$
N
= 2 gauge theories and of minimal surfaces in AdS. We also show that our TBA equations, combined with exact quantization conditions, provide a powerful method to solve spectral problems in Quantum Mechanics. We illustrate our general analysis with a detailed study of PT-symmetric cubic oscillators and quartic oscillators.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference87 articles.
1. R. Balian, G. Parisi and A. Voros, Quartic oscillator, in Feynman path integrals, Springer, Berlin Heidelberg, Germany (1979), pg. 337 [INSPIRE].
2. A. Voros, Spectre de l’équation de Schrödinger et méthode BKW, Publications Mathématiques d’Orsay, France (1981).
3. A. Voros, The return of the quartic oscillator. The complex WKB method, Ann. I.H.P. Phys. Théor.
39 (1983) 211.
4. E. Delabaere and F. Pham, Resurgent methods in semi-classical asymptotics, Ann. I.H.P. Phys. Théor.
71 (1999) 1.
5. H. Dillinger, E. Delabaere and F. Pham, Résurgence de voros et périodes des courbes hyperelliptiques, Ann. Inst. Fourier
43 (1993) 163.
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