Variational Bounds on Scattering Amplitudes for Unphysical Energies

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Abstract
The Kohn-type variational principle for the elements of the scattering matrix is derived in a form which displays the second-order error term explicitly. With the scattering energy taken to be a complex parameter, a calculable bound on the magnitude of this error term is obtained. This allows for a systematic improvement in the accuracy of the variational calculation. The motivation for this study lies in recent demonstrations that accurate analytic continuation to physical energies can in fact be performed. The applicability of this technique to the determination of the level-shift operator and the effective potential is pointed out.