Exact and approximate solutions of Schr?dinger's equation for a class of trigonometric potentials

摘要

The asymptotic iteration method is used to find exact and approximate solutions of Schr?dinger'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 Schr?dinger 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.