Renormalised perturbation theory for a general D-dimensional isotropic anharmonic oscillator

Hypervirial theorems are applied in order to obtain easily perturbation series (PS) for eigenenergies and expected values of power of the radial coordinate of a general D-dimensional isotropic anharmonic oscillator (IAO(D)). In the next step the renormalisation method is introduced to obtain renormalised PS allowing the eigenenergies of IAO(D) to be calculated with a high accuracy in a whole range of quantum numbers n, l and for high anharmonic constants. (author)