# Quantum singular complete integrability

```@article{Paul2014QuantumSC,
title={Quantum singular complete integrability},
author={T. Paul and L. Stolovitch},
journal={arXiv: Mathematical Physics},
year={2014}
}```
• Published 2014
• Mathematics, Physics
• arXiv: Mathematical Physics
We consider some perturbations of a family of pairwise commuting linear quantum Hamiltonians on the torus with possibly dense pure point spectra. We prove that the Rayleigh-Schr{\"o}dinger perturbation series converge near each unperturbed eigenvalue under the form of a convergent quantum Birkhoff normal form. Moreover the family is jointly diagonalised by a common unitary operator explicitly constructed by a Newton type algorithm. This leads to the fact that the spectra of the family remain… Expand
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