The asymptotic iteration method for the eigenenergies of the anharmonic oscillator potential V(x)=Ax2α+Bx2

The asymptotic iteration method is used to calculate the eigenenergies for the anharmonic oscillator potentials V(x)=Ax2α+Bx2 (A>0, B<0), with (α=2) for quartic, and (α=3) for sextic anharmonic oscillators. An adjustable parameter β is introduced in the method to improve its rate of convergence. Comparing the present results with the numerical values calculated by earlier workers, it is found that, asymptotically this method gives exact results over the full range of parameter values, A and B.