Accuracy Tests of the Envelope Theory

TL;DR

This paper evaluates the envelope theory's accuracy in quantum many-body systems, identifying divergence in potentials as a key factor in reduced precision and analyzing the effects of variational properties on improvement methods.

Contribution

The study tests hypotheses explaining the envelope theory's limitations, providing insights into factors affecting its accuracy in quantum systems.

Findings

Divergences in potential reduce accuracy

Lack of variational character diminishes improvement effects

Envelope theory's reliability varies with system properties

Abstract

The envelope theory is an easy-to-use approximation method to obtain eigensolutions for some quantum many-body systems, in particular in the domain of hadronic physics. Even if the solutions are reliable and an improvement procedure exists, the method can lack accuracy for some systems. In a previous work, two hypotheses were proposed to explain the low precision: the presence of a divergence in the potential or the lack of a variational character for peculiar interactions. In the present work, different systems are studied to test these hypotheses. These tests show that the presence of a divergence does indeed cause less accurate results, while the lack of a variational character reduces the impact of the improvement procedure.