Reactive Quantum Scattering in Two Dimensions

<p>In an effort to develop a more efficient time dependent approach for calculating scattering matrix elements absorbing boundary conditions are combined together with the channel packet method. The channel packet method relies on calculating two Moller states: one representing reactants and one representing products. The time dependent correlation function between the two Moller states is efficiently computed by individually propagating the Moller states using absorbing boundary conditions as they exit the interaction region of the potential. As a Moller state evolves in time it will be attenuated by the absorbing boundary conditions without reflecting of the edge of the grid thereby permitting the use of a much smaller grid. The Fourier transform of the correlation function is then used to compute scattering matrix elements. The efficiency of the combination of the channel packet method with absorbing boundary conditions is demonstrated in one dimension through application to the one dimensional square well. The one dimensional square well has an analytic solution which provides a benchmark for testing both the efficiency and accuracy of this approach. Scattering matrix elements obtained using the channel packet method with absorbing boundary conditions are in excellent agreement with the analytic solution. The new approach converges to the correct analytic solution as well as provides a dramatic reduction in grid size. The reduced grid size results in a faster more efficient computation.</p><p>This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact and remains as true to the original work as possible. Therefore you will see the original copyright references library stamps (as most of these works have been housed in our most important libraries around the world) and other notations in the work.</p><p>This work is in the public domain in the United States of America and possibly other nations. Within the United States you may freely copy and distribute this work as no entity (individual or corporate) has a copyright on the body of the work.</p><p>As a reproduction of a historical artifact this work may contain missing or blurred pages poor pictures errant marks etc. Scholars believe and we concur that this work is important enough to be preserved reproduced and made generally available to the public. We appreciate your support of the preservation process and thank you for being an important part of keeping this knowledge alive and relevant.</p>