# Quantum singular complete integrability

@article{Paul2014QuantumSC, title={Quantum singular complete integrability}, author={Thierry Paul and Laurent Stolovitch}, journal={arXiv: Mathematical Physics}, year={2014} }

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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