An example Fluctuating potential curves

The coupled time-dependent Schrodinger equation for the vibrational wavepackets i R,t) and i 2 R,t) on the electronic states 1 and 2, respectively, in a diabatic representation is given as 

For a linearly polarized external field in the dipole approximation, the time-dependent interaction is given by 

The electric field generated by the classical vector potential of the electromagnetic field of a pulse laser to be used in Eq. (5.23) is of the standard form 

This representation is useful since we are considering an external field oscillating with a time-scale comparable to that of the nuclear motion. The diagonal matrix elements of Eq. (5.22) are defined as 

Chemical Theory Beyond the Born-Oppenheimer Paradigm 

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