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Chapter 9 Uncertainty Relations on Homogeneous Groups

  • Michael Ruzhansky
  • Durvudkhan Suragan
Open Access
Chapter
Part of the Progress in Mathematics book series (PM, volume 327)

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.

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Authors and Affiliations

  • Michael Ruzhansky
    • 1
    • 2
    • 3
  • Durvudkhan Suragan
    • 4
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Department of Mathematics: Analysis, Logic and Discrete MathematicsGhent UniversityGhentBelgium
  3. 3.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  4. 4.Department of MathematicsNazarbayev UniversityAstanaKazakhstan

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