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Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory

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Abstract

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schrödinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψits configuration is typically random, with probability density ρgiven by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas.

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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstraße 39, 80333, München, Germany

    Detlef Dürr

  2. Departments of Mathematics, Physics, and Philosophy, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey, 08854-8019

    Sheldon Goldstein

  3. Dipartimento di Fisica dell'Università di Genova, Istituto Nazionale di Fisica Nucleare— Sezione di Genova, via Dodecaneso 33, 16146, Genova, Italy

    Nino Zanghì

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Dürr, D., Goldstein, S. & Zanghì, N. Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory. Journal of Statistical Physics 116, 959–1055 (2004). https://doi.org/10.1023/B:JOSS.0000037234.80916.d0

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