  The asymptotic iteration method is used to find exact and approximate
solutions of Schroedinger's equation for a number of one-dimensional
trigonometric potentials (sine-squared, double-cosine, tangent-squared, and
complex cotangent). Analytic and approximate solutions are obtained by first
using a coordinate transformation to reduce the Schroedinger equation to a
second-order differential equation with an appropriate form. The asymptotic
iteration method is also employed indirectly to obtain the terms in
perturbation expansions, both for the energies and for the corresponding
eigenfunctions.
