From Koopman-von Neumann theory to quantum theory

DOI10.1007/S40509-017-0113-2zbMath1400.81095arXiv1705.07427OpenAlexW3103179333WikidataQ59607316 ScholiaQ59607316MaRDI QIDQ1621545

Ulf Klein

Publication date: 9 November 2018

Published in: Quantum Studies: Mathematics and Foundations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.07427

zbMATH Keywords

quantum theoryLiouville equationderivation of Schrödinger equationKoopman-von Neumann theoryquantum-classical relation

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (13)

A transfer operator approach to relativistic quantum wavefunction ^* ⋮ Unitary representation of the Poincaré group for classical relativistic dynamics ⋮ Classical dynamics from a unitary representation of the Galilei group ⋮ Eisenhart lift of Koopman-von Neumann mechanics ⋮ Madelung transform and probability densities in hybrid quantum–classical dynamics ⋮ Koopman wavefunctions and classical–quantum correlation dynamics ⋮ Momentum maps for mixed states in quantum and classical mechanics ⋮ Quantum dynamics of the classical harmonic oscillator ⋮ Operational classical mechanics: holonomic systems ⋮ The Schwinger action principle for classical systems* ⋮ Projective representation of the Galilei group for classical and quantum–classical systems* ⋮ From quantum hydrodynamics to Koopman wavefunctions. II ⋮ Dynamics of the τ-Wigner distribution function

Cites Work

• Zur Operatorenmethode in der klassischen Mechanik
• Geometric dequantization
• ON KOOPMAN–VON NEUMANN WAVES II
• Hamiltonian Systems and Transformation in Hilbert Space
• ON KOOPMAN–VON NEUMANN WAVES
• Gauge principle revisited: Towards a unification of space–time and internal gauge interactions
• Derivations of the Lie Algebra of Polynomials Under Poisson Bracket
• On the principles of elementary quantum mechanics
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