Mean-field path representation Semiclassical Ehrenfest theory

2 Mean-field path representation Semiclassical Ehrenfest theory 

We next turn to much simpler and easily calculable methods. The semiclassical Ehrenfest theory (SET) is based on rather an intuitive combination of the electronic dynamics on time-dependent nuclear configuration and the Newtonian dynamics of point-like nuclei using the wavepacket average of the Hellmann-Feynman force. 

One of the most powerful methods to study the nonadiabatic transition starts from a time-dependent electronic Schrodinger equation 

SET is known to give very accurate nonadiabatic transition amplitude up to the quantum phases as long as the path, which is driven by the averaged electronic state as in Eq. (4.43), resides in the strong nonadiabatic 

In conclusion, SET is quite useful and promising as a practical means to describe nonadiabatic transitions from the view point of electron dynamics. However the theoretical foundation is weak and therefore it is not easy to improve this theory so as to represent the phenomena of nuclear wavepacket bifurcation. 

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