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POSITION AND MOMENTUM OBSERVABLES ON R AND ON R 3

Claudio Carmeli, Teiko Heinonen, Alessandro Toigo

Published Jan 1, 2004• 19 citations
OpenAlex

Abstract

Abstract. We characterize all position and momentum observables on R and on R 3. We study some of their operational properties and discuss their covariant joint observables. 1.

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In this thesis the structure and properties of imprecise quantum measurements are investigated. The starting point for this investigation is the representation of a quantum observable as a normalized positive operator measure. A general framework to describe measurement inaccuracy is presented. Requirements for accurate measurements are discussed, and the relation of inaccuracy to some optimality criteria is studied. A characterization of covariant observables is given in the case when they are imprecise versions of a sharp observable. Also the properties of such observables are studied. The case of position and momentum observables is studied. All position and momentum observables are characterized, and the joint positionmomentum measurements are discussed.