Vibration of Diatomic System in One-Dimensional Nanomaterials

By means of the hypergeometric series method, the explicit expressions of energy eigenvalues and eigenfunctions of bound states for a diatomic system with a hyperbolic potential function are obtained in the one-dimensional nanomaterials. The eigenfunctions of a one-dimensional diatomic system, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.