Spatial interpretation of "compositeness" for finite-range potentials

TL;DR

This paper explores how the concept of 'compositeness' in quantum bound states relates to the spatial distribution of constituents, specifically in finite-range potentials, linking scattering amplitude to probability densities.

Contribution

It provides a spatial interpretation of compositeness for s-wave bound states in finite-range potentials, connecting scattering data with spatial probability densities.

Findings

Compositeness measures the probability of constituents being separated beyond the interaction range.

The relation holds for spherically symmetric, energy-independent finite-range potentials.

The approach clarifies the physical meaning of compositeness in quantum systems.

Abstract

We discuss the relation between the "compositeness" of an s-wave bound state, as derived from a related partial wave scattering amplitude, and the corresponding spatial probability densities, for the case of spherically symmetric, energy-independent finite-range potentials in non-relativistic quantum mechanics. We find that in this simple case "compositeness" is a measure for the probability to find the constituents separated by a distance greater than the interaction range.