r(D) oscillators with arbitrary D>0 and perturbation expansions with Sturmians

In contrast to widespread belief the current Rayleigh-Schrodinger perturbation theory may provide an easy description of double well oscillators and/or of the strongly anharmonic forces with an arbitrary power-law asymptotical growth. One has only to work in a suitable Sturmian basis. The feasibility and numerical efficiency of the construction is illustrated on a few one-dimensional one-body examples. (C) 1997 American Institute of Physics.