Uncertainty relation for the radial momentum and radial coordinate in the Coulomb potential

TL;DR

This paper derives the uncertainty relations for radial momentum and coordinate in hydrogen atom states, showing minimal uncertainty for circular Rydberg states.

Contribution

It provides the first derivation of uncertainty relations specifically for radial variables in the Coulomb potential, highlighting minimal uncertainty states.

Findings

Minimal uncertainty achieved in circular Rydberg states

Uncertainty relations derived for arbitrary hydrogen atom states

Circular Rydberg states optimize the uncertainty bound

Abstract

We have obtained the uncertainty relations for arbitrary states of the hydrogen atom. It is shown that the minimal value of the uncertainty relation is attained for the circular Rydberg states.