Analytic Quantum Mechanics of Diatomic Molecules with Empirical Potentials

Abstract

The Schrödinger equations of diatomic molecules with empirical potential functions are solved approximately by means of the hypergeometric series method. The potential functions may fit the experimental Rydberg-Klein-Rees curve more closely than the Morse function. Rigorous solutions of Schrödinger equations are also obtained with a similar method for zero total angular momentum. The eigenfunctions of diatomic molecules, expressed in terms of Jacobi polynomial, are employed as the orthonormal basis sets, and analytic expressions of matrix elements for the position and momentum operators are given in closed form.