Abstract
We discuss the question of error estimation in approximate calculations of scattering phase shifts. The Kato integral identity between the exact and approximate solutions is used as the starting point to determine an upper bound to the absolute value of the difference between the exact and approximate result. This bound involves the maximum value of the modulus of the exact wavefunction as a factor. For the potential scattering case it is shown that this maximum occurs in the asymptotic region, if the potential is monotonically decreasing (with decreasing r). For more general potentials simple calculable bounds to the maximum of the wavefunction are derived, for energies which are everywhere higher than the potential. The results are illustrated for scattering by an (attractive) exponential potential and are compared to bounds obtained previously by Bardsley, Gerjuoy, and Sukumar, who have used the Lippman–Schwinger equation to determine bounds to the maximum modulus of the wavefunction.
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