# Quantum spectral problems and isomonodromic deformations

@inproceedings{Bershtein2021QuantumSP, title={Quantum spectral problems and isomonodromic deformations}, author={M. Bershtein and Pavlo Gavrylenko and A. M. Grassi}, year={2021} }

We develop a self-consistent approach to study the spectral properties of a class of quantum mechanical operators by using the knowledge about monodromies of 2 × 2 linear systems (Riemann-Hilbert correspondence). Our technique applies to a variety of problems, though in this paper we only analyse in detail two examples. First we review the case of the (modified) Mathieu operator, which corresponds to a certain linear system on the sphere and makes contact with the Painlevé III3 equation. Then…

## 4 Citations

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Julián Barragán Amado, 2, 3, ∗ Bruno Carneiro da Cunha, † and Elisabetta Pallante 4, ‡ Department of Mathematics, University of Sherbrooke, 2500, boul. de l’Université, Sherbrooke, Quebec, Canada…

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