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In molecular reactions at the microscopic level the appearance of resonanceshas an important influence on the reactivity. It is important to predict when abound state transitions into a resonance and how these transitions depend onvarious system parameters such as internuclear distances. The dynamics of suchsystems are described by the time-independent Schr\"odinger equation and theresonances are modeled by poles of the S-matrix. Using numerical continuationmethods and bifurcation theory, techniques which find their roots in the studyof dynamical systems, we are able to develop efficient and robust methods tostudy the transitions of bound states into resonances. By applying Keller'sPseudo-Arclength continuation, we can minimize the numerical complexity of ouralgorithm. As continuation methods generally assume smooth and well-behavingfunctions and the S-matrix is neither, special care has been taken to ensureaccurate results. We have successfully applied our approach in a number ofmodel problems involving the radial Schr\"odinger equation.

Applying numerical continuation to the parameter dependence of solutions of the Schr\"odinger equation