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arXiv · 2208.05871

The Non-commutative Robertson-Schr\"{o}dinger Uncertainty Principle

Agapitos N. Hatzinikitas
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Abstract

We investigate properties of the covariance matrix in the framework of non-commutative quantum mechanics for an one-parameter family of transformations between the familiar Heisenberg-Weyl algebra and a particular extension of it. Employing as a measure of the Robertson-Schr\"{o}dinger uncertainty principle the linear symplectic capacity of the Weyl ellipsoid (and its dual), we determine its corresponding bounds. Inequalities between the capacities for non-commutative phase-spaces are established. We also present a constructive example based on a simple model to justify our theoretical predictions.

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Agapitos N. Hatzinikitas. 2022-08-11. The Non-commutative Robertson-Schr\"{o}dinger Uncertainty Principle. https://arxiv.org/abs/2208.05871

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