Physics – Mathematical Physics
Scientific paper
2010-11-30
Journal of Computational and Applied Mathematics, Volume 234, Issue 4, 15 June 2010, Pages 1238-1248
Physics
Mathematical Physics
Scientific paper
10.1016/j.cam.2009.07.054
In molecular reactions at the microscopic level the appearance of resonances has an important influence on the reactivity. It is important to predict when a bound state transitions into a resonance and how these transitions depend on various system parameters such as internuclear distances. The dynamics of such systems are described by the time-independent Schr\"odinger equation and the resonances are modeled by poles of the S-matrix. Using numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, we are able to develop efficient and robust methods to study the transitions of bound states into resonances. By applying Keller's Pseudo-Arclength continuation, we can minimize the numerical complexity of our algorithm. As continuation methods generally assume smooth and well-behaving functions and the S-matrix is neither, special care has been taken to ensure accurate results. We have successfully applied our approach in a number of model problems involving the radial Schr\"odinger equation.
Broeckhove Jan
Kłosiewicz Przemysław
Vanroose Wim
No associations
LandOfFree
Applying numerical continuation to the parameter dependence of solutions of the Schrödinger equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Applying numerical continuation to the parameter dependence of solutions of the Schrödinger equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Applying numerical continuation to the parameter dependence of solutions of the Schrödinger equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-445222