Scattering and bound-state trajectories with effective quantum potentials

Fermion Molecular Dynamics (FMD)¹ has been successful in understanding quantum mechanical processes through a simplified quasi-classical treatment using effective quantum potentials that are momentum dependent. These potentials mimic the Heisenberg Uncertainty and Pauli Exclusion principles by excluding the forbidden regions of phase space. Our study aimed at understanding the reason behind the success of this simplified treatment. As a first step, dynamic effects brought in by these potentials in electronic bound-states and scattering were studied. The trajectories differ considerably from their classical counterparts. We report the evolution of the combined momentum-dependent and Coulomb potential for different bound state trajectories which explain the stabilizing effect possible in this treatment. This could be the reason for longer ionization times predicted by FMD that are comparable to experimental results². It is known that classical and quantum studies of Rutherford scattering cross sections result in identical results. We tested the effects of the effective quantum potential on the scattering process. The results differ considerably from classical/quantum results in the large angle scattering regime where the effective quantum potential dominates over the repulsive Coulomb. Non-physical oscillations in the scattering angle are observed indicating extreme sensitivity to the impact parameter for small impact parameters. In all the tests, conservation principles were not violated by the effective potentials.