Complementarity of representations in quantum mechanics

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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 languageAmerican English
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
Issue number1
StatePublished - Mar 2004

ASJC Scopus subject areas

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


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


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