Action Decomposed Function ADF

We adopt the following representation of a nuclear wavefunction on its general Cartesian coordinate q as 

For an extension of ADF to a case including a laser field described by vector potential, [495] we study the following non-relativistic Schrodinger equation for nuclear motion on the coordinates R 

The velocity of a particle is correlated with its momentum in such a way that 

The classical counterpart of this djmamics is represented in the following Hamilton-Jacobi equation 

we evaluate the right hand side in Eq. (6.113). Since the kinetic energy parts are the origin of confusion, we should treat them with some 

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