Canonically Conjugate Pairs, Uncertainty Relations, and Phase Operators
- 1 August 1970
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (8) , 2242-2249
- https://doi.org/10.1063/1.1665388
Abstract
Apparent difficulties that prevent the definition of canonical conjugates for certain observables, e.g., the number operator, are eliminated by distinguishing between the Heisenberg and Weyl forms of the canonical commutation relations (CCR's). Examples are given for which the uncertainty principle does not follow from the CCR's. An operator F is constructed which is canonically conjugate, in the Heisenberg sense, to the number operator; and F is used to define a quantum time operator.Keywords
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