Lattice time-dependent correlated two-electron system approach to scattering problems

This thesis presents a time-dependent approach for the solution of the quantum mechanical three-body problem. The solution presented here is exact in that the approximations are numerical. All the Coulomb interactions between the three particles are taken into account with no approximations. In the time-dependent approach, the quantum mechanical wave functions for the system are obtained at successive times. One of the possible three-body problems is electron-hydrogen scattering. For this case, time-dependent probabilities for exciting the hydrogen atom may be obtained by projecting the states of the target atom onto the time-dependent correlated two-electron wave function. Measurable cross sections for electron impact excitation are obtained at the point where the probabilities are no longer changing with time. The accuracy of this approach is found to be dependent on the total angular momentum. In the lowest total angular momentum, L = 0 case, the angular momentum coupling terms do not contribute and the results compare favorably with those obtained from other methods. However, with increasing total angular momentum, there are numerical instabilities that are associated with the coupling terms. It is found that there is an angular range for the stability of the coupling terms for each total angular momentum. This range greatly reduces with increasing total angular momentum --Abstract, page iii