Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, rho(r) = rho (0), the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, rho(r) = rho (0) r (2), we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and a"" quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of rho (0), in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.