AN OPTIMIZED 2ND-ORDER PERTURBATIVE STUDY OF THE ASYMMETRICAL QUANTUMANHARMONIC-OSCILLATOR

We study the energy eigenvalues of a cubic-quartic anharmonic oscillat or 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 optim ized second-order perturbative calculation is found to yield very accu rate energies especially for the excited states: the asymptotic error is shown to be - 0.002 %. When the same method is applied to an oscill ator with the sextic anharmonic potential x(2)/2 (j=3)Sigma(6) x(j), s imilar accuracy is obtained for the excited states with an asymptotic error of about -0.003 %.