Complementarity of representations in quantum mechanics

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Abstract

We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the canonical commutation relations. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero element.

Original languageEnglish (US)
Pages (from-to)45-56
Number of pages12
JournalStudies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
Volume35
Issue number1
DOIs
StatePublished - Mar 2004

All Science Journal Classification (ASJC) codes

  • History
  • General Physics and Astronomy
  • History and Philosophy of Science

Keywords

  • C*-algebra
  • Complementarity
  • Hidden variables
  • Quantum mechanics

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