We present electronic Raman scattering resutls on a high-quality modulation-doped GaAs single-quantum well. We particularly analyze the change in the transition energy between the lowest, occupied and the first-excited, empty quantum levels as a function of the electron density in the well, which we are able to vary using an additional illumination. This variation is quantitatively reproduced taking into account the corresponding change in the self-consistent electrostatic potential. We thereby get some new insight onto the electron states renormalization in the presence of carriers. © 1989 The American Physical Society.