Pure States and theRepresentation
- 25 April 1969
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 180 (5), 1239-1243
- https://doi.org/10.1103/physrev.180.1239
Abstract
The coherent-state representation for the density operator of the electromagnetic field is studied for the case in which the density operator represents a pure state, . An exact and complete characterization is given of the states for which the representation exists with a weight function that is a tempered distribution. These states form an exceedingly narrow class: each may be generated from a particular coherent state by the application of a finite number of creation operators, i.e., , where and the are arbitrary complex numbers. For them the weight function is a linear combination of the two-dimensional delta function and a finite number of its derivatives. For other pure states, the function has singularities that are not compatible with the form of the representation.
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