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Complementarity of representations in quantum mechanics

Halvorson, Hans (2001) Complementarity of representations in quantum mechanics. [Preprint]

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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 CCRs. 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.


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      Item Type: Preprint
      Keywords: complementarity, Bohr, canonical commutation relations, Weyl algebra
      Subjects: Specific Sciences > Physics > Quantum Mechanics
      Depositing User: Hans Halvorson
      Date Deposited: 16 Oct 2001
      Last Modified: 07 Oct 2010 11:10
      Item ID: 444
      URI: http://philsci-archive.pitt.edu/id/eprint/444

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