Date of Award
Doctor of Philosophy (PhD)
Department of Engineering Physics
David E. Weeks, PhD
The interaction picture is used together with the channel-packet method in a new time-dependent approach to compute reactive scattering matrix elements. The channelpacket method enables the use of the interaction picture for computing reactive S-matrix elements by splitting the computational effort into two parts. First, asymptotic reactant and product wavepackets are individually propagated into the interaction region of the potential to form Moller states. The interaction picture, in contrast to the usual Schrödinger picture of quantum mechanics, is so constructed that a wavefunction that experiences no change in potential (that is, a free-particle wavefunction) remains always fixed, with no translation or distortion. In the Schrödinger picture, free-particle wavefunctions translate and spread with time. By removing free-particle spreading, the use of the interaction picture reduces the size of the region of space that must be modeled when computing the Moller states. Since the asymptotic wavepackets are propagated in time independently of each other, it is possible to choose an asymptotic Hamiltonian and corresponding interaction picture that is well suited for each arrangement channel. By using two different interaction pictures, one for the reactant arrangement channel and one for the product arrangement channel, it is possible to realize savings in the required grid size. During the second part of the channel-packet computation, the reactant and product wavepackets obtained from the first part of the calculation are further propagated using the Schrödinger picture. The time-dependent correlation between the evolving wavepackets is calculated as they split into energetically accessible arrangement channels and are absorbed using absorbing boundary conditions. The use of the interaction picture for computing S-matrix elements is developed, validated, and illustrated using a simple one-dimensional reactive example where the size of the grid required for computing the M0ller state in the interaction picture is reduced by a factor of two when compared with required grid size in the Schrödinger picture. Larger reductions in grid requirements are realized when the wavepackets remain compact while evolving into Möller states, especially when reactant or product momenta are high.
DTIC Accession Number
MacLachlan, Michael J., "Application of the Interaction Picture to Reactive Scattering in One Dimension" (1999). Theses and Dissertations. 4825.