Abstract
We study the energy eigenvalues of a cubic-quartic anharmonic oscillator with the operator method introduced by Feranchuk and Komarov (Ann. Phys. (N.Y.), 238 (1995) 370). Based on the minimization of the second-order perturbative correction and the energy-variance, a simple optimized second-order perturbative calculation is found to yield very accurate energies especially for the excited states: the asymptotic error is shown to be -0.002 %. When the same method is applied to an oscillator with the sextic anharmonic potentialx2 /2 + X%j, i = » similar accuracy is obtained for the excited states with an asymptotic error of about -0.003%.
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