  The binding energy and the corresponding wave function of excitons in
GaAs-based finite square quantum wells (QWs) are calculated by the direct
numerical solution of the three-dimensional Schroedinger equation. The precise
results for the lowest exciton state are obtained by the Hamiltonian
discretization using the high-order finite-difference scheme. The microscopic
calculations are compared with the results obtained by the standard variational
approach. The exciton binding energies found by two methods coincide within 0.1
meV for the wide range of QW widths. The radiative decay rate is calculated for
QWs of various widths using the exciton wave functions obtained by direct and
variational methods. The radiative decay rates are confronted with the
experimental data measured for high-quality GaAs/AlGaAs and InGaAs/GaAs QW
heterostructures grown by molecular beam epitaxy. The calculated and measured
values are in good agreement, though slight differences with earlier
calculations of the radiative decay rate are observed.
