Heisenberg’s uncertainty principle associated with the Caputo fractional derivative

In this paper, we establish the Heisenberg’s uncertainty inequality associated with the Caputo derivative of order q ∈ (1, ∞) in the generalized Bargmann–Fock space. We also determine exactly when the equality occurs in the uncertainty inequality. It is done by estimating the growth of the eigenvalu...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2021-04, Vol.62 (4)
Main Author: Lian, Pan
Format: Article
Language:English
Subjects:
Commutators
Eigenvalues
Inequality
Physics
Uncertainty principles
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we establish the Heisenberg’s uncertainty inequality associated with the Caputo derivative of order q ∈ (1, ∞) in the generalized Bargmann–Fock space. We also determine exactly when the equality occurs in the uncertainty inequality. It is done by estimating the growth of the eigenvalues of the commutator [Dq,zq]. We prove that the sequence of eigenvalues of [Dq,zq] tends to ∞ when the fractional order q belongs to (1, ∞). However, the sequence converges to zero when q belongs to (0, 1), which shows different behavior. Hence, only a weak uncertainty inequality is obtained for the latter case.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0038691