Covariant localizations in the torus and the phase observables

Abstract

We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is furnished and the commutative localizations are singled out. As a consequence, we also get a vector sequence characterization of the covariant phase observables.

16 pages, no figure, Latex2e

References in corpus (1)

• Are Number and Phase Complementary Observables?

Cited by in corpus (13)

• Are Number and Phase Complementary Observables?
• Covariant fuzzy observables and coarse-graining
• The norm-1-property of a quantum observable
• Positive sesquilinear form measures and generalized eigenvalue expansions
• The Pegg-Barnett Formalism and Covariant Phase Observables
• On the structure of covariant phase observables
• A note on infinite extreme correlation matrices
• Covariant phase difference observables
• A dilemma in representing observables in quantum mechanics
• Optimal covariant measurements: the case of a compact symmetry group and phase observables
• The phase representation of covariant phase observables
• Extreme phase and rotated quadrature measurements
• Noise sequences of infinite matrices and their applications to the characterization of the canonical phase and box localization observables