Dynamics in the electron-nuclear quantum-classical mixed representation

3 Dynamics in the electron-nuclear quantum-classical mixed representation 

The d3mamics of electron wavepackets is determined by the time dependent variational principle 

With the above Hamiltonian, Eq. (6.10), an analogy to purely classical mechanics brings about the canonical equations of motion for nuclear classical variables (R, P) as [492] 

These equations are also defined in the nuclear configuration space and 

To use this operator in practice, we should transform it to a matrix form by sandwiching two electronic states, say, ( / and j) as 

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