Rayleigh–Schrödinger perturbation expansions for eigenvalues E(λ) of nonlinear Hamiltonians of the form Ĥ(0)+λ〈r p〉rq, p,q≥1 are calculated using hypervirial (HV) and Hellmann–Feynman (HF) theorems. Such Hamiltonians are similar in form to those employed in the study of ‘‘self‐interacting’’ systems, e.g., solute–solvent interactions. The specific cases considered for H(0) are one‐dimensional harmonic oscillators and hydrogen atoms. The eigenvalue expansions for the nonlinear problems are compared with those of the linear problems where p=0, whose large‐order behavior and summability properties are well‐known. Also examined are the perturbation expansions for the expectation values 〈rk〉, which are also products of the HVHF method.
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