International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 |
International Tables for Crystallography (2010). Vol. B, ch. 5.2, p. 648
Section 5.2.5. Projection approximation – real-space solution^{a}Department of Applied Physics, Royal Melbourne Institute of Technology, 124 La Trobe Street, Melbourne, Victoria 3000, Australia,^{b}Arizona State University, Box 871504, Department of Physics and Astronomy, Tempe, AZ 85287–1504, USA, and ^{c}School of Physics, University of Melbourne, Parkville, Australia |
Many of the features of the more general solutions are retained in the practically important projection approximation in which is replaced by its projected mean value , so that the corresponding Hamiltonian does not depend on z. Equation (5.2.4.1b) can then be solved directly by iteration to give and the solution may be verified by substitution into equation (5.2.4.1a).
Many of the results of dynamical theory can be obtained by expansion of equation (5.2.5.1) as followed by the direct evaluation of the differentials. Such expressions can be used, for instance, to explore symmetries in image space.