Quantum equilibrium and the role of operators as observables in quantum theory

Detlef Dürr, Sheldon Goldstein, Nino Zanghì

Research output: Contribution to journalArticlepeer-review

71 Scopus citations


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 ψ its configuration is typically random, with probability density ρ given 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.

Original languageEnglish (US)
Pages (from-to)959-1055
Number of pages97
JournalJournal of Statistical Physics
Issue number1-4
StatePublished - Aug 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Bohm's causal interpretation of quantum theory
  • Bohmian experiment
  • POVM
  • formal measurements
  • foundations of quantum mechanics
  • genuine measurement
  • hidden variables
  • pilot wave
  • quantum equilibrium
  • quantum observables


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