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A general procedure based on shift operators is formulated to deal withanharmonic potentials. It is possible to extract the ground state energyanalytically using our method provided certain consistency relations aresatisfied. Analytic expressions for the exact ground state energy have alsobeen derived specifically for a large class of the one-dimensional oscillatorwith cubic-quartic anharmonic terms. Our analytical results can be used tocheck the accuracy of existing numerical methods, for instance the method ofstate-dependent diagonalization. Our results also agree with the asymptoticbehavior in the divergent pertubative expansion of quartic harmonic oscillator.Comment: LaTeX with six figure (gif) files; Submitted to Phys. Rev.

Analytic expression for exact-ground-state energy based on an operator method for a class of anharmonic potentials