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A general theory of the extended x-ray absorption edge fine structure is given within the framework of a one-electron approximation. An approximate evaluation of this theory is proposed which allows a simple calculation of the spectrum starting from theoretically calculated electron-atom scattering phase shifts. This is shown to agree quite well with the observed spectrum for copper in the energy range 200-800 eV above the K edge without the use of any adjustable parameters. A qualitative evaluation of multiple scattering effects in the general theory is made which should be reasonably good below 100 eV. Multiple scattering corrections are found to be very important in the low-energy region of the spectrum for close-packed structures. It is shown that significant cancellation of single scattering amplitudes can occur which could account for detailed anomalies in the spectrum of Cu found by Stern, Sayers, and Lytle.