Complete Integrability of Quantum and Classical Dynamical Systems
- Authors: Volovich I.V.1
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 11, No 4 (2019)
- Pages: 328-334
- Section: Research Articles
- URL: https://journals.rcsi.science/2070-0466/article/view/201324
- DOI: https://doi.org/10.1134/S2070046619040071
- ID: 201324
Cite item
Abstract
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 of scattering theory and wave operators are given.
About the authors
Igor V. Volovich
Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: volovich@mi-ras.ru
Russian Federation, Moscow
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