Characteristics of the Wave Function of Coupled Oscillators in Semiquantum Chaos

Using the method of adiabatic invariants and the Born-Oppenheimer approximation, we have successfully got the excited-state wave functions for a pair of coupled oscillators in the so-called \textit{semiquantum chaos}. Some interesting characteristics in the \textit{Fourier spectra} of the wave functions and its \textit{Correlation Functions} in the regular and chaos states have been found, which offers a new way to distinguish the regular and chaotic states in quantum system.