2019/11/04 by И. В. Волович, Volovich, Igor V. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1911.01335
openalex publication_date 2019/11/04 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian\nis unitary equivalent to a set of non-interacting classical harmonic\noscillators and in this sense any quantum dynamics is completely integrable.\nHigher order integrals of motion are presented. That does not mean that we can\nexplicitly compute the time dependence for expectation value of any quantum\nobservable. A similar result is indicated for classical dynamical systems in\nterms of Koopman's approach. Explicit transformations of quantum and classical\ndynamics to the free evolution by using direct methods of scattering theory and\nwave operators are considered. Examples from classical and quantum mechanics,\nand also from nonlinear partial differential equations and quantum field theory\nare discussed. Higher order integrals of motion for the multi-dimensional\nnonlinear Klein-Gordon and Schrodinger equations are mentioned.\n