A short note on minimal length

TL;DR

This paper explores the origin of minimal length in atomic and nuclear systems, linking it to fundamental interaction strength and Compton wavelength, and provides a formula consistent with existing upper-bound estimates.

Contribution

It proposes a new formula connecting minimal length to fundamental interaction parameters, offering insights into its origin in atomic and nuclear contexts.

Findings

Derived a formula for minimal length based on interaction strength and Compton wavelength.

Numerical results align with previously estimated upper bounds.

Provides a theoretical basis for understanding minimal length in quantum systems.

Abstract

After revival of the concept of minimal length, many investigations have been devoted, in literature, to estimate upper-bound on minimal length for systems like hydrogen atom, deuteron etc. We report here a possible origin of minimal length for atomic and nuclear systems which is connected with the fundamental interaction strength and the Compton wavelength. The formula we appear at is numerically close to the upper-bounds found in literature.