Quantum Mechanics and the Generalized Uncertainty Principle

TL;DR

This paper explores how the generalized uncertainty principle arises in a quantum mechanical model with discrete position eigenvalues, highlighting its implications for minimal uncertainty wave packets.

Contribution

It introduces a simple quantum model with discrete position eigenvalues to demonstrate the emergence of the generalized uncertainty principle.

Findings

Generalized uncertainty principle results for minimum uncertainty wave packets.

Discrete position eigenvalues lead to modified uncertainty relations.

Insights into quantum gravity effects on quantum mechanics.

Abstract

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.