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