Phase Shifts of Bound State Waves Scattered at Classical Turning Points: Morse Potential

The analytical transfer matrix method suggests a new quantization condition for calculating bound state eigenenergies exactly. In the quantization condition, the phase shifts of bound state wave functions scattered at classical turning points are explicitly introduced. We calculate the phase shifts of eigenfunctions of the Morse potential with various boundary conditions in order to understand the physical meaning of phase shifts. The Morse potential is known to adequately describe the interaction energy between two atoms and, therefore, it is frequently used to determine the vibrational energy levels of diatomic molecules. The variation of Morse potential eigenenergies influenced upon by changing boundary conditions is also investigated.