Résumé:

In Bohmian quantum mechanics, both Schrödinger's wavefunction and an ensemble of quantum trajectories are propagated together to describe the evolution of a given system. Said trajectories are driven by anadditional, fully quantum potential deduced from the "pilot" wave function. Displacement of the trajectory ensemble symmetrically dictates the evolution of the wave function. However a recent reformulation allows the exclusive use of the trajectory ensemble to modelize the scattering process. The resulting equations of motion for the trajectories can be put in an Hamiltonian form, with coupled first order ODEs describing exactly the behaviour of a 1D time-independent process. In this case, propagation of a single trajectory is sucient to completely characterize the system. This ecient procedure ( great stability and accuracy ) was applied to scattering processes through simple potential barrier model and more recently in a quantum capture model of ultra-cold chemical reaction. I will highlight the virtues of this approach when applied to scattering through multiple potential barriers. In this more complex situation often encountered in chemistry, coupling with metastable states breaks themonotonicity of the cumulated reaction probability prole through the presence of resonance peaks. Strong interference patterns are observed inbetween the barrier and necessitate the use of an adaptative ODE solving procedure. Numerical simulations will be presented both on system models and on a 1D-reaction path hamiltonian model of ketene izomerisation for which conventional quantum mechanical calculations (using grid methods and absorbing boundary conditions) are available. I will also present how Hamiltonianform allows for a straightforward extension of the one-dimensional quantum formalism to multidimensional processes through the use of hybrid quantum-classical trajectories. The efficiency of this dual-level theorywill be illustrated on the ketene isomerization process.