A Unification of Quantum and Classical Mechanics through Ehrenfest Theorems

          @misc{ scivideos_PIRSA:12010167,
            doi = {10.48660/12010167},
            url = {https://pirsa.org/12010167},
            author = {Bondar, Denys},
            keywords = {Quantum Foundations},
            language = {en},
            title = {A Unification of Quantum and Classical Mechanics through Ehrenfest Theorems},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2012},
            month = {jan},
            note = {PIRSA:12010167 see, \url{https://scivideos.org/pirsa/12010167}}
          }
          

Abstract

We present a quantization method based on theEhrenfest theorem embedded in an extended algebraic structure capableof consistently describing hybrid quantum-classical systems, where thestandard quantum and classical mechanics are two limiting cases. TheWigner phase space formulation and the Schordinger equation are foundto be two alternative representations of the quantum case while theKoopman-von Neumann equation is the corresponding classicalcounterpart. Moreover, the developed quantization procedure isgeneralized to describe open systems, quantum/classical field theoriesand relativistic mechanics where new dynamical equations appear,shedding new light on important practical problems such asunderstanding of the quantum/classical transition and modeling ofmesoscopic systems.

Related references: arXiv:1105.4014, arXiv:1112.3679, arXiv:1107.5139