Analytic expression for exact-ground-state energy based on an operator method for a class of anharmonic potentials
نویسندگان
چکیده
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground-state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact-ground-state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharmonic terms. Our analytical results can be used to check the accuracy of existing numerical methods, for instance the method of state-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of the quartic harmonic oscillator.
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