The Non-commutative Robertson-Schrödinger Uncertainty Principle

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 uncertai...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Author: Hatzinikitas, Agapitos N
Format: Article
Language:English
Subjects:
Covariance matrix
Principles
Quantum mechanics
Uncertainty principles
Online Access:Get full text
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Summary: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.
ISSN:2331-8422