The closed orbit theory allows for the semiclassical calculation of photoabsorption spectra and eigenenergies. However, simple shooting and bisection methods are restricted to the calculation of short closed orbits in systems with smooth potentials like the hydrogen atom in a constant magnetic field.

A systematic closed orbit search is achieved by application of a multishooting algorithm combined with symbolic dynamics. With this method, nearly arbitrarily long and extremly unstable orbits can be found. About 16 million orbits have been calculated for the diamagnetic hydrogen atom. They provide a basis to obtain the resonance spectrum and, with the help of the harmonic inversion method, individual eigenenergies and dipole matrix elements.