Derivation of Exact Eigenvalues and Eigenfunctions Based on the Analytical Transfer Matrix Method

We extend the analytical transfer matrix method (ATMM) to calculate both the energy eigenvalues and wavefunctions for the Morse potential and the regulated Coulomb potential. Derivations of the exact eigenenergies and eigenfunctions are presented in detail by the ATMM. We compare our results with that obtained by relaxational approach and the eigenvalue moment method, and it is shown that the ATMM can produce accurate eigenvalues. The eigenfunctions by the ATMM are also proven to be correct and meaningful.