# Quantum-classical correspondence via Liouville dynamics. I. Integrable systems and the chaotic spectral decomposition

@article{Wilkie1997QuantumclassicalCV, title={Quantum-classical correspondence via Liouville dynamics. I. Integrable systems and the chaotic spectral decomposition}, author={Joshua Wilkie and Paul Brumer}, journal={Physical Review A}, year={1997}, volume={55}, pages={27-42} }

A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the cancellation of essential singularities, is demonstrated. The application to chaotic systems requires an understanding of classical Liouville eigenfunctions and a Liouville spectral decomposition, developed herein. General approaches to the construction of these…

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## References

SHOWING 1-10 OF 33 REFERENCES

### Stochastic behavior in classical and quantum hamiltonian systems : Volta Memorial Conference, Como, 1977

- Physics
- 1979

Integrable and stochastic behaviour in dynamical astronomy.- Adiabatic and stochastic motion of charged particles in the field of a single wave.- Numerical study of particle motion in two waves.-…

### The Principles of Quantum Mechanics

- PhysicsNature
- 1947

IT is now twenty years since the theory of quantum mechanics was founded, and not much less since the first edition of Dirac's book was published. Ever since, it has been a classic of scientific…

### Quantum mechanics

- PhysicsNature
- 1975

Quantum Mechanics for Organic Chemists.By Howard E. Zimmerman. Pp. x + 215. (Academic: New York and London, May 1975.) $16.50; £7.90.

### Phys

- 82, 2330
- 1985

### J. Chem. Phys

- J. Chem. Phys
- 1985