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arXiv · 2308.15934

Uncertainty relation for non-Hermitian operators

Fabio Bagarello
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Abstract

In this paper we discuss some aspects of the Heisenberg uncertainty relation, mostly from the point of view of non self-adjoint operators. Some equivalence results, and some refinements of the inequality, are deduced, and some relevant examples are discussed. We also begin a sort of {\em dynamical analysis} of the relation, in connection with what has been recently called $\gamma$-{dynamics} and $\gamma$-symmetries, and we discuss in some details the role of different scalar products in our analysis. The case of self-adjoint operators is recovered as a special case of our general settings.

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Fabio Bagarello. 2023-08-30. Uncertainty relation for non-Hermitian operators. https://arxiv.org/abs/2308.15934

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