An inequality for a periodic uncertainty constant

TL;DR

This paper establishes a refined inequality for the periodic uncertainty constant, linking it to the non-periodic case, and explores a minimization problem for the Heisenberg uncertainty constant.

Contribution

It introduces a new inequality for the periodic uncertainty constant and extends the connection between periodic and non-periodic uncertainty measures.

Findings

Refined lower bound for the periodic uncertainty constant.

Extended connection between periodic and non-periodic uncertainty constants.

Analyzed a minimization problem for the Heisenberg uncertainty constant.

Abstract

An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A particular minimization problem for a non-periodic (Heisenberg) uncertainty constant is studied.