We report a calculation of the absorption coefficient of donor impurities located at the center of a quasi‐1D GaAs quantum well wire with finite confinement potential as a function of photon energies for different wire widths. The theory has been formulated by using suitable variational wave functions. In the presence of a uniform magnetic field applied along the axis of the wire, there is an enhancement in the absorption peak as the size of the wire is increased and a reduction of this peak as the magnetic field is increased. We see clearly that the effect of confinement is more important compared to the effect of the magnetic field. A comparison with the infinite barrier potential is also investigated.