A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and extends its capabilities. Specifically, the Schwinger variational approach gives results without the divergences that need to be regularized in other methods. Furthermore, it provides a framework to identify the origin of these singularities and possibly improve the local frame transformation. We have used the method to obtain the scattering parameters for different confining potentials symmetric in $x,y$. The method is also used to treat photodetachment processes in the presence of various confining potentials, thereby highlighting effects of the infinitely many closed channels. Two general features predicted are the vanishing of the total photoabsorption probability at {it every} channel threshold and the occurrence of resonances below the channel thresholds for negative scattering lengths. In addition, the case of negative ion photodetachment in the presence of uniform magnetic fields is also considered where unique features emerge at large scattering lengths.
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