Applying numerical continuation to the parameter dependence of solutions of the Schrodinger equation

作者：Broeckhove Jan; Klosiewicz Przemyslaw^*; Vanroose Wim

来源：Journal of Computational and Applied Mathematics, 2010, 234(4): 1238-1248.

DOI：10.1016/j.cam.2009.07.054

• Pseudo-arclength continuation
• Bifurcation theory
• Dynamical systems
• Quantum resonances
• Scattering theory
• Schrodinger equation
• S-matrix pole trajectories

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 Schrodinger 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 Schrodinger equation.

• 出版日期2010-6-15