Wavepackets coordinate space motion

Finally, Gaussian wavepacket methods are described in which the nuclear wavepacket is described by one or more Gaussian functions. Again the equations of motion to be solved have the fomi of classical trajectories in phase space. Now, however, each trajectory has a quantum character due to its spread in coordinate space. 

Figure 13. The (a) ground and (b) excited- electronic-state Bom-Oppenheimer potential surfaces. The n/2 pulse moves half of the initial amplitude, y(O), from a surface a to surface b. After the pulse the nuclear wavefunctions of the ground-state and excited-state surfaces are denoted x Ui) and r (ti (b) Wavepacket evolution of xb. Motion of the wavepacket causes the overlap of the ground-state wavefunction and the excited-state wavefunction to decay, resulting in free induction decay. x remains in place in coordinate space, (c) The n pulse exchanges the amplitude of surface a with surface b. (

Figure 9.1 Motion of a wavepacket in coordinate space. Panels (a) - (f) depict six times in the evolution of an initially Gaussian wavepacket. The wavepacket is launched at the Franck-Condon point of a repulsive potential surface of a Y-X-Y triatomic molecule. The v coordinate (symmetric stretch) is bound and the u coordinate (antisymmetric stretch) is unbound. The wavepacket oscillates along v (the first partial recurrence is in frame e) and spreads along u (from Heller, 1978).

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