The Born Rule in Quantum and Classical Mechanics

Details The Born Rule in Quantum and Classical Mechanics The Born Rule in Quantum and Classical Mechanics

2006-04-24

arxiv.org/abs/quant-ph/0604178v1

Phys. Rev. A 73, 052109 (2006)

Physics

Quantum Physics

5 pages, no figures, to appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.73.052109

Considerable effort has been devoted to deriving the Born rule (e.g. that $|\psi(x)|^2 dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

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