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.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics