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Infinite Dimensional Analysis Quantum Probability and Related Topics

ON ACCARDI'S NOTION OF COMPLEMENTARY OBSERVABLES

Gianni Cassinelli, Veeravalli S. Varadarajan

Published Jun 1, 2002• 16 citations
Publisher

Abstract

We discuss some examples of complementary observables, in the sense of Accardi. We show that the trace property is not sufficient to determine such a pair of observables.
DOI
10.1142/s0219025702000754

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In this note we show that the momentum and position operators of μμμ-deformed quantum mechanics for μ>0μ> 0μ>0 are not Accardi complementary in a sense that we will define. We conjecture that this is also true if −1/2<μ<0-1/2 < μ< 0−1/2<μ<0.