Bound energies and states of the Yukawa potential through matrix representation

Abstract

We use the basis expansion method to solve the Schrödinger equation with the Yukawa potential, which is popular in most areas of physics but which cannot be solved analytically. This method is based on the basic principle in quantum physics that all particle states are represented by the complete set of eigenbases. We use the Coulomb eigenstates as a basis set for a particle state under the Yukawa potential and find the bound energies within more accuracy than ever using matrix representation. We justified the validity of this method in the choice of coupling constant of the Coulomb potential and in the choice of the number of bases included in the numerical calculation. We present the eigenenergies for [Formula: see text] states and compare our results to published ones. We find that the results are relatively precise with relative errors less than 2.2%. Our method is very efficient in a sense that all bound energies and eigenstates are obtained at the same time, which is not tried in other methods. The precision in calculation should be taken at least smaller than the energy difference between states.