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

• URL: http://arxiv.org/abs/2208.05871v1
• Date: Thu, 11 Aug 2022 15:18:02 GMT
• Title: The Non-commutative Robertson-Schr\"{o}dinger Uncertainty Principle
• Authors: Agapitos N. Hatzinikitas
• Abstract summary: Inequalities between the capacities for non-commutative phase-spaces are established. We present a constructive example based on a simple model to justify our predictions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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