Nuclear wavepacket description of femtosecond time-resolved photoelectron spectroscopy

3 Nuclear wavepacket description of femtosecond time-resolved photoelectron spectroscopy 

To describe photoionization in a pump-probe context, the total wavefunc-tion of our system, r,R,t), may be decomposed into several neutral electronic states n(r R), whose dynamics we wish to probe, and several ionized states ( i R) use for probing, 

The electronic wavefunctions represent the eigenstates of the electronic Hamiltonian P at each nuclear position and are orthonormalized, e.g.. 

The electronic wavefunctions are time-independent but depend parametrically on the nuclear coordinates, while the time dependence is explicit in the nuclear wavefunctions, Xn R,t) and Xc,k R,t), associated with the neutral and ionized electronic states, respectively. 

In the following, we explicitly write out the coupled Schrodinger equation for the case of one neutral and one ionized state extension to any number of states is formally straightforward. Resorting to the dipole approximation, we aim to write the time-dependent Schrodinger equation for the nuclear wavefunctions in the form. 

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