Quantum chaos and order based on classically moving reference frames

We develop a mathematically consistent approach for treating the quantum systems based on moving classical reference frames. The classical and quantum exact solutions show excellently classical-quantum correspondence, in which the quantum chaotic coherent states correspond to the classically chaotic motions. Applying the approach to the periodically driven linear and nonlinear oscillators, the regular and chaotic quantum states and quantum levels, and the quantum chaotic regions are evidenced. The results indicate that chaos may cause the collapse of matter wave packets and suppress the quantum effect of energy.