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A new scheme of approximation in quantum theory is proposed which ispotentially applicable to arbtrary interacting systems. The method consists inin approximating the original Hamiltonian by one corresponding to a suitableexactly solvable system (with interaction) such that the "quantum average" ofboth are equal, thus forcing self-consistency.The method transcends thelimitations of the variational method and the perturbation theory.The resultsare systematically improvable by the construction of a improved perturbationtheory (IPT) which automatically satisfies the condition of convergence.Uniformly accurate results are obtained for the case of the quartic-,sextic-and octic anharmonic oscillators as well as the quartic and sextic double welloscillators. The leading order results reproduce earlier results by differentmethods using different input assumptions.The results for the sexticoscillators agree well with exact prediction of supersymmetry. We also discussthe stability and structure of the effective vacuum state of the approximation.Comment: 41 Pages, 1 Figure, pdf-forma

A NEW GENERAL APPROXIMATION SCHEME IN QUANTUM THEORY: APPLICATION TO THE ANHARMONIC AND THE DOUBLE WELL OSCILLATORS