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A novel general approximation scheme (NGAS) is proposed, which is potentiallyapplicable for arbitrary strength of interaction in quantum theory. The schemeutilizes an input Hamiltonian, which is exactly solvable. The effects ofinteraction are incorporated into the input Hamiltonian through a non-linearfeedback mechanism by self-consistency requirements. The method isnonperturbative, yet improvable in a new formulation of perturbation theory,designated as: mean field perturbation theory (MFPT). We apply the scheme toanharmonic interactions in one dimension and obtain uniformly accurate resultsby Borel summation, for the quartic-, sextic-, octic-anharmonic oscillators andto the quartic double-well oscillator (QDWO) for arbitrary strength ofcoupling. The results for the QDWO may be contrasted with those from thestandard formulation of perturbation theory , where Borel-summation fails evenfor small values of the coupling strength.

Investigations of Interacting Quantum Systems in a Novel General Approximation Scheme (NGAS)