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/
