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By R. Brill and R. Mason (Eds.)

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Czech. J. of Physics, B 11, 199 (1961). , Czech. J. of Physics, B 12,538 (1962). , Czech. J. of Physics, B 12, 764 (1962). , C. R. Acad. Sci. Paris, 251, 2502 (1960). , J. of Appl. Cryst. (1968), 1, 181. , Philips Research Rpts, 18, 413 (1963). , C. R. Acad. Sci. Paris, 261, 3774 (1965). , Physica Statu Solidi, 26, 469 (1968). Sommerfeld, Partial Differential equations. Academic Press, p. 52 (1949). Hattori, H. , J. Phys. Soc. Japan, 21, 1772(1966). Authier, A. and Malgrange, C, C. R. Acad. Sci.

5) and AT is proportional to MM0, that is to the parameter 77 which we have defined (equation (II-4-3)) to characterize the departure from Bragg' law of a plane wave. Let us introduce a function D® equal to £> 1. Equation (IV-4-1) shows that D'hs and Z>£ are Fourier transforms. This result is very important since it shows as well that the solutions £>£ 46 A. Authier and D^ of the propagation equation for incident plane and spherical waves respec­ tively are proportional to Fourier transforms.

1 Bethe's Theory The dynamical theory of electron diffraction was developed by Bethe [19] in 1928. It was the aim of this theory to solve Schrodinger's equation inside a crystal plate, extended infinitely in two dimensions, adapting the solutions at the boundary faces to one incident plane wave and a set of diffracted plane waves leaving the surfaces into the vacuum. We will briefly recapitulate here this theory. Neglecting for the moment the dyna­ mics of the crystal particles (nuclei and electrons), we regard the potential energy in Schrodinger's equation as a static one, V(r) = - e • 0(r), acting on the scattered electron at the point r.

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