Correspondence principles: the relationship between classical trajectories and quantum spectral

The general correspondence principle specifies a relationship between wave functions and families of trajectories. For bounded systems with regular trajectories, this general correspondence principle leads to the principle of quantization of action. The general principle also leads to a correspondence principle for finite-resolution spectra: oscillation in the average density of states, or in the average oscillator strength as a function of energy, are connected to periodic or to closed orbits. This principle holds independently or whether classical trajectories are orderly or chaotic