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Position uncertainty measures on the sphere. (English) Zbl 1072.81037

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5–12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 211-224 (2004).
Summary: Position uncertainty (delocalization) measures for a particle on the sphere are proposed and illustrated on several examples of states. The new measures are constructed using suitably the standard multiplication angle operator variances. They are shown to depend solely on the state of the particle and to obey uncertainty relations of the Schrödinger-Robertson type. A set of Hermitian operators with continuous spectrum is pointed out the variances of which are complementary to the longitudinal angle uncertainty measure.
For the entire collection see [Zbl 1048.53002].

MSC:

81S05 Commutation relations and statistics as related to quantum mechanics (general)
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81R30 Coherent states
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