Analytical solution of the stationary one-dimensional Schroedinger equation

New algorithms are derived and the software composed for fast computing of the one-dimensional wave functions in the range of a continuous energy spectrum. The method can be applied to calculate the quantum-mechanical Franck-Condon factors and the fine structure of the optical spectra of simple quantum systems. This enables to improve the real potential energy curves of such systems, which is demonstrated for diatomic xenon molecules. (author)