Approximate Analytical Solution of the Yukawa Potential with Arbitrary Angular Momenta

The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov–Uvarov method, we obtain approximate analytical solutions of the radial Schr?dinger equation for the Yukawa potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods. Also, we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.