# 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} }

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…

## 3 Citations

### On Integrability of Dynamical Systems

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- 2020

A classical dynamical system may have smooth integrals of motion and not have analytic ones; i.e., the integrability property depends on the category of smoothness. Recently it has been shown that…

### Effective Heisenberg equations for quadratic Hamiltonians

- Physics, MathematicsInternational Journal of Modern Physics A
- 2022

We discuss eﬀective quantum dynamics obtained by averaging projector with respect to free dynamics. For unitary dynamics generated by quadratic fermionic Hamiltonians we obtain eﬀective Heisenberg…

### Quadratic conservation laws for equations of mathematical physics

- MathematicsRussian Mathematical Surveys
- 2020

Linear systems of differential equations in a Hilbert space are considered that admit a positive-definite quadratic form as a first integral. The following three closely related questions are the…

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