Research on the new form of higher-order generalized uncertainty principle in quantum system

TL;DR

This paper introduces a novel high-order generalized uncertainty principle that modifies quantum operators, aligns with quantum gravity concepts, and explores its implications on localization states and the harmonic oscillator.

Contribution

It proposes a new form of high-order GUP consistent with quantum gravity, analyzing its effects on quantum states and systems.

Findings

Maximum localization states are derived.

Position eigenfunctions are characterized.

Implications for the harmonic oscillator are discussed.

Abstract

This paper proposes a new high-order generalized uncertainty principle, which can modify the momentum operator and position operator simultaneously. Moreover, the new form of GUP is consistent with the viewpoint of the existence of the minimum length uncertainty and the maximum observable momentum proposed by the mainstream quantum gravity theory. By using the new GUP, the maximum localization state and position eigenfunction are discussed, and the corresponding conclusions are compared with the existing literature. The harmonic oscillator is further discussed at the end of this article as an example.