On two classes of perturbations: Role of signs of second-order Rayleigh-Schr\"odinger energy corrections

TL;DR

This paper analyzes two classes of perturbation problems based on the signs of second-order energy corrections in Rayleigh-Schrödinger theory, highlighting the likelihood of negative corrections and their implications for matrix perturbations.

Contribution

It distinguishes two classes of perturbation problems and explains why negative second-order energy corrections are more probable in standard Rayleigh-Schrödinger perturbation theory.

Findings

Negative second-order corrections are more probable in standard perturbation theory.

The classes differ in reproducing finite-dimensional matrix perturbation results.

Discussion includes analytical insights into perturbation behaviors.

Abstract

We distinguish two extreme classes of perturbation problems depending on the signs of second-order energy corrections and argue why it is generally much more probable to obtain a negative value of the same for any state in the standard Rayleigh-Schr\"odinger perturbation theory. The classes are seen to differ in reproducing results of finite-dimensional matrix perturbations. A few related issues are also discussed, some of which are based on available analytical results.