Abstract
In this chapter we discuss relations between main operators of quantum mechanics, that is, relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups as well as their consequences. Since in most uncertainty relations and in these operators the appearing weights are radially symmetric, it turns out that these relations can be extended to also hold on general homogeneous groups. In particular, we obtain both isotropic and anisotropic uncertainty principles in a refined form, where the radial derivative operators are used instead of the elliptic or hypoelliptic differential operators.
Chapter PDF
Author information
Authors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2019 The Author(s)
About this chapter
Cite this chapter
Ruzhansky, M., Suragan, D. (2019). Chapter 9 Uncertainty Relations on Homogeneous Groups. In: Hardy Inequalities on Homogeneous Groups. Progress in Mathematics, vol 327. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02895-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-02895-4_10
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-02894-7
Online ISBN: 978-3-030-02895-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)