Corpus ID: 233481847

Quantum spectral problems and isomonodromic deformations

  title={Quantum spectral problems and isomonodromic deformations},
  author={M. Bershtein and Pavlo Gavrylenko and A. M. Grassi},
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… Expand

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