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The existence of periodic orbit bunches is proven for the diamagnetic Keplerproblem. Members of each bunch are reconnected differently at self-encountersin phase space but have nearly equal classical action and stability parameters.Orbits can be grouped already on the level of the symbolic dynamics byapplication of appropriate reconnection rules to the symbolic code in theternary alphabet. The periodic orbit bunches can significantly improve theefficiency of semiclassical quantization methods for classically chaoticsystems, which suffer from the exponential proliferation of orbits. For thediamagnetic hydrogen atom the use of one or few representatives of a periodicorbit bunch in Gutzwiller's trace formula allows for the computation ofsemiclassical spectra with a classical data set reduced by up to a factor of20.

Semiclassical quantization of the diamagnetic hydrogen atom with near action-degenerate periodic-orbit bunches