Abstract
A procedure based on the piecewise perturbation treatment of the Schrödinger equation is developed. The procedure is shown to be convergent for any bounded perturbation. A simple way to construct the algorithm is also developed, which can be used for any potential of polynomial form. Our procedure is further particularized for the anharmonic-oscillator potential U(x)=m2x2+2λx2α (λ>0 and integer α2) and applied to produce highly accurate numerical values for its energy levels. The experimental results also show that this procedure exhibits almost equal efficiency for all relevant values of the principal quantum number n, mass parameter m2, coupling λ, and anharmonicity α.