The theory of a rectangular quantum well in an external electric field is formulated in terms of surface Green function matching. This yields both the Green function and the wavefunction, and provides a practical method for the calculation of physical properties. The limits of validity of the equivalent-infinite-well approximation are studied. Applications to finite wells include the analysis of experimental data on the Stark shift of exciton peaks and quenching of the photoluminescence by the external field. The importance of an accurate estimate of the wavefunction for the electro-optical properties is stressed and demonstrated in practical terms.