Born rule in quantum and classical mechanics

  title={Born rule in quantum and classical mechanics},
  author={Paul Brumer and Jiangbin Gong},
  journal={Physical Review A},
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. 

Chapter 26 Derivations of the Born Rule

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

Derivations of the Born Rule

  • L. Vaidman
  • Philosophy
    Jerusalem Studies in Philosophy and History of Science
  • 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

From probabilistic mechanics to quantum theory

  • U. Klein
  • Physics
    Quantum Studies: Mathematics and Foundations
  • 2019
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton’s function, which determines canonical equations, a

Hilbert space theory of classical electrodynamics

Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics

Operational dynamic modeling transcending quantum and classical mechanics.

It is shown that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory, and should provide a basis for formulating novel theories.

Quantum/Classical Interface: Fermion Spin

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

Quantum Mechanics as a Theory of Incompatible Symmetries

It is increasingly becoming recognized that incompatible variables, which play an essential role in quantum mechanics (QM), are not in fact unique to QM. Here we add a new example, the “Arrow”

Many-Body Systems and Quantum Hydrodynamics

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.



The statistical interpretation of quantum mechanics

The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of

Statistical Interpretation of Quantum Mechanics.

The published work for which the honor of the Nobel prize for the year 1954 has been accorded to me does not contain the discovery of a new phenomenon of nature but, rather, the foundations of a new

Quantum Mechanics: Foundations and Applications

I Mathematical Preliminaries.- I.1 The Mathematical Language of Quantum Mechanics.- I.2 Linear Spaces, Scalar Product.- I.3 Linear Operators.- I.4 Basis Systems and Eigenvector Decomposition.- I.5

Non-equilibrium statistical mechanics

In the preceding chapter we discussed the microscopic foundations of extended irreversible thermodynamics through fluctuation theory. The present chapter deals with more general methods of

Lectures on Theoretical Physics

Vorlesungen über theoretische PhysikVon Prof. Arnold Sommerfeld. Band 1: Mechanik. Vierte, neubearbeitete Auflage. Pp. xii + 276. 18 D. marks. Band 2: Mechanik der deformierbaren Medien. Pp. xv + 376


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  • 2005


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  • 1997


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  • 2004

Non equilibrium statistical mechanics

In part I of these lecture notes, I introduce the basic tools of non equilibrium statistical mechanics: linear response, Brownian motion, Langevin equation, (Pauli) master equation. Part II is

T he ei genval ues can be ei ther conti nuous or di screte, dependi ng on the system . For exam pl e, the spectrum com pri ses i ntegers w hen