The Morse potential eigenenergy by the analytical transfer matrix method

Using the analytical transfer matrix method in combination of supersymmetry algebra, we have analytically derived the eigenenergies of the Morse potential. The derived eigenenergies are, of course, identical with previously known values. The analytical transfer matrix method is found to be exact and useful for understanding the nature of bound states. And the highest bound state possible in the Morse potential is mathematically determined without ambiguity.