Liouville-von Neumann approach and time-dependent Gaussian approximation

@article{Kim2002LiouvillevonNA,
  title={Liouville-von Neumann approach and time-dependent Gaussian approximation},
  author={Hyeong-Chan Kim and Jae Hyung Yee},
  journal={arXiv: High Energy Physics - Theory},
  year={2002}
}
We show that Liouville-von Neumann approach to quantum mechanical systems, which demands the existence of invariant operators, reproduces the time-dependent variational Gaussian approximation. We find the effective action of the time-dependent systems and show that many aspects of the dynamics are independent of the details of time evolution, e.g., the squeezing of the wave-function is determined by the effective potential of the final stage of time-evolution. 

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