TBA equations and quantization conditions

Yoan Emery (Université de Genève, 30, quai Ernest-Ansermet, Genève 4, CH-1211, Switzerland)

It has been recently realized that, in the case of polynomial potentials, the exact WKB method can be reformulated in terms of a system of TBA equations. In this paper we study this method in various examples. We develop a graphical procedure due to Toledo, which provides a fast and simple way to study the wall-crossing behavior of the TBA equations. When complemented with exact quantization conditions, the TBA equations can be used to solve spectral problems exactly in Quantum Mechanics. We compute the quantum corrections to the all-order WKB periods in many examples, as well as the exact spectrum for many potentials. In particular, we show how this method can be used to determine resonances in unbounded potentials.

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Published on:
23 July 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 7
Pages 1-76
DOI:
https://doi.org/10.1007/JHEP07(2021)171
arXiv:
2008.13680
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: