  In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the
`asymptotic iteration method' for solving second-order homogeneous linear
differential equations. In this paper, we study perturbed problems in quantum
mechanics and we use the method to find the coefficients in the perturbation
series for the eigenvalues and eigenfunctions directly, without first solving
the unperturbed problem.
