In this study, for the first time, we probe the influences of the external electric and magnetic field (EF and MF) on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of quantum well (QW) with the Rosen-Morse (RM) potential confinement constituting by GaAs/GaAlAs heterostructure. To do this, the bound state energies and the wave functions of the Rosen-Morse quantum well (RMQW) under the influence of the external EF and MF are determined by solving the corresponding wave equation using the diagonalization method within the framework of the effective mass approach and the parabolic band approximation. As the purpose of the present work is to find out the functionality of the external EF and MF on TRICs and TACs of RMQW, same RMQW with V-1 = 250 meV, V-2 = 228 meV, eta = 0.01 cm(-1) is taken into consideration throughout the work. The TRICs and TACs of RMQW in the weak and strong regimes of the external fields are discussed in detail. The present work introduces to researches that how to and in what regimes apply the EF and MFs to be considered in devices designs and applications including RMQW.