A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Operator integrals and phase space observables
Tekijät: Lahti P, Pellonpaa JP, Ylinen K
Kustantaja: AMER INST PHYSICS
Julkaisuvuosi: 1999
Lehti: Journal of Mathematical Physics
Tietokannassa oleva lehden nimi: JOURNAL OF MATHEMATICAL PHYSICS
Lehden akronyymi: J MATH PHYS
Vuosikerta: 40
Numero: 4
Aloitussivu: 2181
Lopetussivu: 2189
Sivujen määrä: 9
ISSN: 0022-2488
DOI: https://doi.org/10.1063/1.532858
Tiivistelmä
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].
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