How quantum bound states bounce and the structure it reveals

TL;DR

This paper explores how quantum bound states reflect from hard surfaces, revealing insights into nuclear, semiconductor, and cold atom systems through theoretical and numerical analysis of elastic reflection and universal potentials.

Contribution

It introduces a general theory of elastic reflection for composite quantum bodies and derives a universal effective potential for shallow two-body states.

Findings

Numerical ab initio calculations for alpha particle compression.

Universal results for two-body state reflection.

Derived a universal effective potential for shallow states.

Abstract

We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and cold atomic few-body systems on optical lattices with sharp boundaries. We develop the general theory of elastic reflection for a composite body from a hard wall. On the numerical side we present ab initio calculations for the compression of alpha particles and universal results for two-body states. On the analytical side we derive a universal effective potential that gives the reflection scattering length for shallow two-body states.