A sequential analogy is drawn between classes of perturbative theories of quantum fields (superrenormalized, renormalized, and unrenormalized) and the behavior of the matrix elements in Rayleigh-Schr$\stackrel{..}{o}$dinger progressions for an anharmonic oscillator with a perturbation of $\lambda|x|^{-\nu}$. Each class of fields has its own range of values or the parameter $\nu$ for the case of even solutions of the Schr$\stackrel{..}{o}$dinger equation. The proposed analogy is different from those previously examined in the literature.
Department of Theoretical Physics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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