THE ASYMPTOTIC ITERATION METHOD FOR THE EIGENENERGIES OF THE ASYMMETRICAL QUANTUM ANHARMONIC OSCILLATOR POTENTIALS $V(x)=\sum_{j=2}^{2\alpha}A_{j}x^{j}$

Abstract

The asymptotic iteration method is used to calculate the eigenenergies for the asymmetrical quantum anharmonic oscillator potentials [Formula: see text], with (α = 2) for quartic, and (α = 3) for sextic asymmetrical quantum anharmonic oscillators. An adjustable parameter β is introduced in the method to improve its rate of convergence. Comparing the present results with the exact numerical values, and with the numerical results of the earlier works, it is found that asymptotically, this method gives accurate results over the full range of parameter values Aj.