A simple algorithm for the numerical solution of the Schroedinger equation for a one-dimensional problem with a generic potential and its practical implementation in a computer program (called Kmonodim) is presented. This approach allows the study of bound states and can be used in a laboratory course of quantum chemistry to study simple model problems or real systems for which analytical solutions cannot be obtained. The Kmonodim program is written using the C++ and Fortran languages: the management of the input and output data is performed through a graphical user interface (GUI) written using the QT/KDE libraries of the Linux KDE graphical client. The program is freely distributed under the GNU General Public License.