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.

中文翻译：

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量子和经典动力系统的完全可积性

证明了带有任何自伴随哈密顿量的薛定谔方程是酉等价于一组非相互作用的经典谐振子，从这个意义上说，任何量子动力学都是完全可积的。提出了运动积分。用考夫曼的动力系统方法证明了经典动力系统的类似陈述。给出了使用散射理论和波算符的直接方法将量子和经典动力学显式归约到谐振子族的例子。