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The asymptotic iteration method is used to calculate the eigenenergies for the asymmetrical quantum anharmonic oscillator potentials $V(x)=\sum_{j=2}^{2\alpha}A_{j}x^{j}$, 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. [ABSTRACT FROM AUTHOR]

The asymptotic iteration method is used for Dirac and Klein–Gordon equations with a linear scalar potential to obtain the relativistic eigenenergies. A parameter, ς = 0, 1, is introduced in such a way that one can obtain Klein–Gordon bound states from Dirac bound states. It is shown that this method asymptotically gives accurate results for both Dirac and Klein–Gordon equations. [ABSTRACT FROM AUTHOR]

The semirelativistic wave equation which appears in the theory of relativistic quark-antiquark bound states, is cast into a constituent second order Schrödinger-like equation with the inclusion of relativistic corrections up to order (υ/c)² in the quarks speeds. The resulting equation is solved via the Shifted-l expansion technique (SLET), which has been recently developed to get eigenvalues and wave functions of relativistic and nonrelativistic wave equations. The Coulomb, Oscillator, and the Coulomb-plus-linear potentials used in q&qmacr; phenomenology are tested. It is observed that, the energy eigenvalues can be explained well upon the more commonly used nonrelativistic models, when such a dynamical relativistic corrections are introduced. In particular, it provides a remarkable accurate and simple analytic expression for the Coulomb ground-state energy problem, a result which is in the right direction at least to serve as a test of this approach. [ABSTRACT FROM AUTHOR]