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In this contribution, we introduce numerical continuation methods andbifurcation theory, techniques which find their roots in the study of dynamicalsystems, to the problem of tracing the parameter dependence of bound andresonant states of the quantum mechanical Schr\"odinger equation. We extendprevious work on the subject to systems of coupled equations. Bound andresonant states of the Schr\"odinger equation can be determined through thepoles of the S-matrix, a quantity that can be derived from the asymptotic formof the wave function. We introduce a regularization procedure that essentiallytransforms the S-matrix into its inverse and improves its smoothnessproperties, thus making it amenable to numerical continuation. This allows usto automate the process of tracking bound and resonant states when parametersin the Schr\"odinger equation are varied. We have applied this approach to anumber of model problems with satisfying results.

Numerical Continuation of resonances and bound states in coupled channel Schr\"odinger equations