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We distinguish two extreme classes of perturbation problems depending on thesigns of second-order energy corrections and argue why it is generally muchmore probable to obtain a negative value of the same for any state in thestandard Rayleigh-Schr\"odinger perturbation theory. The classes are seen todiffer in reproducing results of finite-dimensional matrix perturbations. A fewrelated issues are also discussed, some of which are based on availableanalytical results.

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