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Without resorting to a circular argument? You are asking too much. However, this probability distribution is perfectly described by considering a component wave model wherein coherence of the component waves correlates with peaks in the probability distribution--i.e. Bragg's Law. IANAM (I am not a mathematician), but, if pressed, I would posit that one could decompose the fun description just a little bit and consider the lattice not as *groups* of reflecting planes, but as individual planes. In such a case, each single reflecting plane would contribute a probability distribution with an angular dependence. The total probability distribution would then be the sum of the probability distributions for every plane in the lattice. Your next question might be, "what's the probability distribution for a single plane". Well, I would imagine that it has a maximum where the angle of incidence equals the angle of reflection and that the phase of a component probability distributions is spatially (i.e. angularly) directly related to the phase of the originating photon. The sum distribution of the reflected photon takes into account the angular phase dependence of its components and so one gets positive and negative interference between component distributions. James Jacob Keller wrote: > Yes, but why should the directions of diffraction conditions be most probable (one of your premises)? > > ==============Original message text=============== > On Fri, 24 Aug 2007 4:54:53 pm CDT James Stroud wrote: > > Here's a fun way to think of it: > > A photon hits a crystal and will diffract off in a certain direction > with the same energy as the original photon. The direction is subject to > a probability distribution based on the lattice, with angles at the > diffraction conditions being most likely and the broadness of the peaks > in the distribution arising from imperfections in the lattice. The > photon propagates as this probability distribution and then is forced to > select from the distribution because we stuck a detector up. The > diffraction pattern we observe is the sum of many such photons > interacting with the crystal. -- James Stroud UCLA-DOE Institute for Genomics and Proteomics Box 951570 Los Angeles, CA 90095 http://www.jamesstroud.com/