Perturbation theory for nonlinear time-independent Schrödinger equations

Péter R. Surjn, Jnos Ngyn

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A special nondegenerate perturbation theory is developed for solving the "nonlinear Schrödinger equation" of the type [H+V()]=E, which arises, e.g., from the study of the environmental effects on molecules. The interaction operator is taken as V()=A|B|. The in vacuo problem H= is considered the zeroth-order description. For the perturbed energies and wave functions recursive formulas are derived at any order of the perturbation. The formulas obtained are compared to the usual Rayleigh-Schrödinger perturbation theory where V is supposed to be independent of . The formal results are applied to the case of the Onsager cavity model.

Original languageEnglish
Pages (from-to)45-48
Number of pages4
JournalPhysical Review A
Issue number1
Publication statusPublished - Jan 1 1983


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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