A1 Refereed original research article in a scientific journal
Operator integrals and phase space observables
Authors: Lahti P, Pellonpaa JP, Ylinen K
Publisher: AMER INST PHYSICS
Publication year: 1999
Journal:Journal of Mathematical Physics
Journal name in sourceJOURNAL OF MATHEMATICAL PHYSICS
Journal acronym: J MATH PHYS
Volume: 40
Issue: 4
First page : 2181
Last page: 2189
Number of pages: 9
ISSN: 0022-2488
DOI: https://doi.org/10.1063/1.532858
Abstract
The operator integral integral f dE of a complex valued measurable function f with respect to a positive operator measure E is considered. If F is a Neumark dilation of E into a projection measure, then the "projected'' operator integral pr(integral fdF) is a restriction of the operator integral f dE. Necessary and sufficient conditions for the equality pr( integral f dF) = integral f dE are obtained. The results are applied to determine the moment operators of the phase space observables generated by the number states. (C) 1999 American Institute of Physics. [S0022-2488(99)01104-4].
The operator integral integral f dE of a complex valued measurable function f with respect to a positive operator measure E is considered. If F is a Neumark dilation of E into a projection measure, then the "projected'' operator integral pr(integral fdF) is a restriction of the operator integral f dE. Necessary and sufficient conditions for the equality pr( integral f dF) = integral f dE are obtained. The results are applied to determine the moment operators of the phase space observables generated by the number states. (C) 1999 American Institute of Physics. [S0022-2488(99)01104-4].
UTU Research Portal