Quantum wavepacket dynamics with trajectories: wavefunction synthesis along quantum paths

The quantum trajectory method (QTM) for wavepacket dynamics involves integration of the quantum hydrodynamic equations for fluid elements (particles) [C. Lopreore and R.E. Wyatt, Phys. Rev. Lett. 82 (1999) 5190]. In this study, it is shown how the wavefunction modulus and phase (action function) may be computed from information carried by the particles as they move along quantum trajectories. The action function is computed by integrating the quantum Lagrangian along the particle trajectories. For a model collinear reaction, plots are presented for the time evolving probability density, Lagrangian, and action function.