Influence of the extent of the eigenstates of a system on the resonances formed through its coupling to a field

TL;DR

This paper investigates how the spatial extent of a particle's eigenstates influences the formation and properties of resonances when coupled to a massless boson field, considering confined and potential well systems.

Contribution

It introduces a detailed analysis of resonance behavior in systems with confined particles and finite potential wells, highlighting the impact of eigenstate extent on resonance widths.

Findings

Resonances depend on the size of the confining region.

Additional resonances appear when the confining radius is comparable to the particle's Compton wavelength.

Resonance widths vary with the extent of the particle's wave functions.

Abstract

We examine resonances for two systems consisting of a particle coupled to a massless boson's field. The field is the free field in the whole space. In the first system, the particle is confined inside a ball. We show that besides the usual energy levels of the particle, which have become complex through the coupling to the field, other resonances are to be taken into account if the ball's radius is comparable to the particle's Compton wavelength. In the second system, the particle is in a finite-depth square-well potential. We study the way the resonances' width depends on the extent of the uncoupled particle's wave functions. In both cases, we limit ourselves to considering two levels of the particle only.