Illustrative application to a two-state model

We now unify the theory of electron wavepackets on the non-Born-Oppenheimer branching paths (PSANB) and the nuclear wavepacket dynamics running along these paths (ADF). This is readily done as 

To avoid unnecessary complexity and confusion, we here study an illustrative two-state nonadiabatic quantum wavepacket dynamics, the adiabatic potential functions of which are drawn in Fig. 6.17. 

This system was artificially modeled based on the ab initio potential curves of LiH molecule. [493] The spatial distribution of the nonadiabatic coupling element is superposed on the two potential curves. In this system, 

We explore two physical events in this system One is a vibrational decay through the nonadiabatic coupling, the initial wavepacket of which is prepared at the left chff of the lower curve (i = 2, with the initial momentum hk = 25). The other one is a collision event, with an initial packet coming in from the dissociation channel (from R = 7, with hk = —45). For these events, we construct the total wavepacket states with PSANB-ADF-NVG according to Eq. (6.147). These total wavefunctions are projected onto the nuclear configuration space and thereby compared with the full quantmn nuclear wavepacket attained through the standard method, Eq. (6.5). 

The full quantum nuclear wavepacket to be compared as a reference is a Gaussian function initially prepared at a position Rq, with the initial wave number ko. The width is set to = 10//co so as to be in the same order of its corresponding de Broglie wave length. The explicit form is 

---