  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.
