Lower Limit for the Energy Derivative of the Scattering Phase Shift
1955/04/01 by Eugene P. Wigner, E. P. Wigner · 2,008 citations
Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #Causality (physics) #Crystallography and Radiation Phenomena #Derivative (finance) #Energy (signal processing) #High-pressure geophysics and materials #Limit (mathematics) #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Phase (matter) #Physics #Quantum mechanics #Scattering #X-ray Diffraction in Crystallography
paper · doi:10.1103/physrev.98.145
published in Physical Review 98(1), 145-147 (American Institute of Physics)
openalex publication_date 1955/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract
It is shown that the derivative of the scattering phase shift with respect to energy, \fracd\ensuremathηdE, must exceed a certain limit if the interaction of scattered particle and scatterer vanishes beyond a certain distance. This limitation of \fracd\ensuremathηdE is, fundamentally, a consequence of the principle of causality; it is derived, however, from a property of the derivative matrix R.
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