Complete Integrability of Quantum and Classical Dynamical Systems

@article{Volovich2019CompleteIO,
  title={Complete Integrability of Quantum and Classical Dynamical Systems},
  author={Igor V. Volovich},
  journal={p-Adic Numbers, Ultrametric Analysis and Applications},
  year={2019},
  volume={11},
  pages={328-334}
}
  • I. Volovich
  • Published 1 October 2019
  • Physics, Mathematics
  • p-Adic Numbers, Ultrametric Analysis and Applications
It is proved that the Schrödinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Integrals of motion are presented. A similar statement is proved for classical dynamical systems in terms of Koopman’s approach to dynamical systems. Examples of explicit reduction of quantum and classical dynamics to the family of harmonic oscillators by using direct methods… 

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