Generalized Cauchy-Schwarz inequality and Uncertainty Relation

TL;DR

This paper introduces a generalized Cauchy-Schwarz inequality and applies it to quantum mechanics, resulting in a modified uncertainty relation and insights into minimum uncertainty wave packets.

Contribution

The paper presents a novel generalized Cauchy-Schwarz inequality and demonstrates its application to modify the quantum uncertainty relation.

Findings

Modified uncertainty relation derived

New form of minimum uncertainty wave packet

Potential implications for quantum measurement

Abstract

A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.