Semirelativistic Bound States: (Pseudo-) Spinless-Salpeter Approaches Reassessed

TL;DR

This paper reassesses semirelativistic bound state models, comparing simplified equations to rigorous spectral constraints to evaluate their accuracy in describing bound states across physics and chemistry.

Contribution

It provides a critical evaluation of various semirelativistic bound state equations using spectral constraints, highlighting their validity and limitations.

Findings

Simplified models can approximate bound state spectra effectively.

Certain equations accurately predict the number and location of eigenstates.

The approach offers a benchmark for assessing bound state approximations.

Abstract

Relativistic quantum field theory offers, in form of the homogeneous Bethe-Salpeter framework, a (Poincar\'e-covariant) description of bound states in terms of their underlying theory's fundamental degrees of freedom. In view of the intrinsic complexity of this approach, simplifications have been sought and abundantly found. The significance of these latter approximations may be estimated by comparing their predictions with (easily inferable) rigorous constraints on the bound-state spectra, such as existence, number and location of discrete eigenstates. The application of these techniques to selected proposed bound-state equations is exemplified for a large class of generalizations of the Hellmann potential frequently employed in several areas of science such as physics and chemistry.