Semiclassical Double-Inequality on Heisenberg Uncertainty Relation in 1D

TL;DR

This paper proves a double-inequality relating position and momentum uncertainties for bound states in one-dimensional quantum systems within the semiclassical limit.

Contribution

It introduces a new double-inequality for the Heisenberg uncertainty product specific to 1D quantum bound states in the semiclassical regime.

Findings

Establishes a rigorous double-inequality for uncertainties

Applicable to a broad class of 1D quantum systems

Enhances understanding of uncertainty relations in semiclassical physics

Abstract

We prove a double-inequality for the product of uncertainties for position and momentum of bound states for 1D quantum mechanical systems in the semiclassical limit.