Classical probabilistic transport equations are reformulated as quantum systems whose wave function obeys Schrödinger evolution and whose observables include non-commuting operators for statistical quantities.
Quantum particles from coarse grained classical probabilities in phase space
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abstract
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.
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2026 1verdicts
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Quantum mechanics for classical transport equations
Classical probabilistic transport equations are reformulated as quantum systems whose wave function obeys Schrödinger evolution and whose observables include non-commuting operators for statistical quantities.