# Born rule in quantum and classical mechanics

@article{Brumer2006BornRI, title={Born rule in quantum and classical mechanics}, author={Paul Brumer and Jiangbin Gong}, journal={Physical Review A}, year={2006}, volume={73}, pages={052109} }

Considerable effort has been devoted to deriving the Born rule [i.e., that {psi}(x){sup 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 classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

## 20 Citations

### Chapter 26 Derivations of the Born Rule

- Philosophy
- 2020

The Born rule, a cornerstone of quantum theory usually taken as a postulate, continues to attract numerous attempts for its derivation. A critical review of these derivations, from early attempts to…

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The Born rule, a cornerstone of quantum theory usually taken as a postulate, continues to attract numerous attempts for its derivation. A critical review of these derivations, from early attempts to…

### From probabilistic mechanics to quantum theory

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Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of…

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### Many-Body Systems and Quantum Hydrodynamics

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This chapter introduces the Born-Oppenheimer approximation used both to devise electronic structure methodologies and to deal with many degree-of-freedom systems within the open quantum theory scenario and a description of Hirschfelder’s approach to quantum equations of change.

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