Analytic expression for exact-ground-state energy based on an operator method for a class of anharmonic potentials - art. no. 052107

A general procedure based on shift operators is formulated to deal with anh armonic potentials. It is possible to extract the ground-state energy analy tically using our method provided certain consistency relations are satisfi ed. Analytic expressions for the exact-ground-state energy have also been d erived specifically for a large class of the one-dimensional oscillator wit h cubic-quartic anharmonic terms. Our analytical results can be used to che ck the accuracy of existing numerical methods, for instance the method of s tate-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of the quartic harmonic osc illator.