Solving for three-dimensional central potentials using numerical matrix methods

Abstract

We present a numerical matrix method to find quantum stationary states and energies for three-dimensional central forces. The method can be used both for familiar, exactly solvable potentials and for those that are not solvable by analytical methods. As examples, we include the Coulomb potential, the finite spherical well, and the Yukawa potential. This method requires much less mathematical expertise than traditional analytical methods, although it does require some familiarity with numerical matrix diagonalization software.