Some equivalences between the auxiliary field method and the envelope theory

TL;DR

This paper demonstrates that the auxiliary field method and envelope theory, two analytical techniques for solving quantum eigenequations, are fundamentally equivalent, enhancing understanding of both methods.

Contribution

It establishes the complete equivalence between the auxiliary field method and envelope theory in solving quantum eigenequations.

Findings

Shows the equivalence between the auxiliary field method and envelope theory.

Provides a deeper understanding of both analytical solution frameworks.

Clarifies the principles underlying each method.

Abstract

The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles \textit{a priori}. This equivalence leads to a deeper understanding of both frameworks.