Exact and approximate solutions of Schroedinger's equation for a class of trigonometric potentials

TL;DR

This paper applies the asymptotic iteration method to find exact and approximate solutions of Schrödinger's equation for various trigonometric potentials, enhancing analytical and perturbative approaches in quantum mechanics.

Contribution

It introduces a systematic approach using the asymptotic iteration method for solving Schrödinger's equation with specific trigonometric potentials, including perturbation expansions.

Findings

Exact solutions for certain potentials

Approximate energy and eigenfunction expansions

Effective coordinate transformations for differential equations

Abstract

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.