The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, paying attention to the natural domains of these unbounded operators. The results are then applied to conveniently determine the moment operators of the Cartesian margins of the phase space observables.

arXiv:0809.0424Journal of Mathematical PhysicsNov 1, 20085 citations

Reports on Mathematical Physics

The moment operators of phase space observables and their number margins

PEKKA J. LAHTI, Maciej Mączyński, Kari Ylinen

Published Jun 1, 1998• 24 citations

Publisher

DOI: 10.1016/s0034-4877(98)80019-0

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The theory of operator integrals is used to determine the moment operators of the Cartesian margins of the phase space observables generated by the mixtures of the number states. The moments of the

x

-margin are polynomials of the position operator and those of the

y

-margin are polynomials of the momentum operator.