Hi Fellows, Zbi's response has addressed refs and the technical complexities that arise when describing the scattering process on a microscopic QM basis.
I shall tell you why I decided to provide this probabilistic QM interpretation. First, a probabilistic approach to empirical science is the overarching theme of the book. Examples range from Bayes to ML and necessarily, the interpretation of quantum mechanics. Having been tortured in Vienna as experimental physicist with instruments that Boltzmann built and probably already Schrödinger broke, when I saw for the first time these explanations of Bragg's equation (footnote *) where 2 incoming, interfering waves are pictured, I was confused. Can't be. The first fact to drive across is that there is no coherence between the photons emitted from a conventional source (and under normal operations with exceptions and caveats I am not going into, also from synchrotrons): In demonstrations with a laser and a diffraction slide, invariably a fraction of students exposed to these Bragg drawings seem to erroneously but justifiably assume that the coherence of the laser is relevant to diffraction. It is the monochromaticity and the brilliance of the laser that makes the experiment work so well, not any necessity for coherence between incoming photons. This is why I avoided throughout the book to show illustrations with 2 incoming waves or wave vectors, as observant readers may have noticed. Second, as a fundamental principle, a macroscopic phenomenon based on the average of many microscopic processes taking place on a quantum mechanical scale can often be well explained with a 'classical' picture. That is why this partial wave recombination business for structure factors works. For me a more logical and consistent approach is to treat diffraction as a probabilistic phenomenon, with the underlying probability distribution simply given by the structure factors. Also the square proportionality between |F| and I follows naturally from quantum mechanics as the observable of these complex probability functions. So, this quantum mechanical interpretation (note the word interpretation) is very consistent and imho unforced and almost beautiful. But, as noted, the underlying microscopic process description is less than trivial, and defies our macroscopic experience. And beauty is in the eye of the beholder.... Historically, of course, when the first diffraction images were taken and the Braggs began to make sense of the images, QM was in its infancy. The ultraviolet catastrophe was fresh in the minds, and the photoelectric effect published only in 1905. The Bohr model came out in 1913, and it took about another 10+ years for Heisenberg, Schroedinger & Cie. to come up with workable theories. So, the Braggs are excused, but today I think a more modern picture involving the underlying QM picture can be presented. * If you are interested in the philosophical issues w/o becoming a quantum physicist, there are interesting accounts about the early history of quantum mechanics which I find a most fascinating period in physics. I can provide a few refs off board later when I am back at my library. So, yes I am guilty of not providing a more concise intro to QM, but as Dirty Harrys says: 'Man's gotta know his limits' Best, BR * [The brilliance of the Bragg equation imho is to combine the 3 independent Laue equations (unhandy) by simply turning the Laue 'pictures' so that reflection on lattice planes - much more intuitive - can be used to relate the diffraction angle (nota bene, not the direction anymore) to lattice spacings.] -----Original Message----- From: CCP4 bulletin board [mailto:[email protected]] On Behalf Of Zbyszek Otwinowski Sent: Friday, May 22, 2015 4:40 AM To: [email protected] Subject: Re: [ccp4bb] X-rays and matter (the particle-wave picture) The answer to your questions depends on the level of understanding of quantum mechanics. I am sending info where to find the subject discussed in more details. Bernhard Rupp's book page 251 necessarily simplifies a rather complex subject of the photon's interaction with multiple particles. Quantum mechanical wave function can be considered virtual from the measurement process point of view, as the photon (a single quantum) appears in the detector during the measurement process, but not on the way to it. > the photon's coherence length The concept of photon's coherence length involves quantum mechanics mixed state. For introduction see: http://en.wikipedia.org/wiki/Quantum_state#Mixed_states > virtual waves Quantum mechanical wave function is "virtual" in certain sense. The Feynman Lectures on Physics Vol 3 covers this subject quite well. > appears again in some direction This refers to quantum mechanical wave-particle duality > Hello Everybody! > I was trying to make some sense from Bernhard Rupp's book page 251. > > I will copy the relevant part... > > When photons travel through a crystal, either of two things can > happen: (i) nothing, which happens over 99% of the time; (ii) the > electric field vector induces oscillations in all the electrons > coherently within* the photon's coherence length* ranging from a few 1000 Angstroms for X-ray emission lines to several microns for modern synchrotron sources. At this point, the > photon ceases to exist, and we can imagine that the electrons > themselves emanate *virtual waves*, which constructively overlap in certain directions, and interfere destructively in others. The scattered photon then *appears again in some direction*, with the probability of that appearance proportional to the amplitude of the combined, resultant scattered wave in that particular direction.......The sum of all scattering > events of independent, single photons then generates the diffraction pattern. > > I underlined the problematic parts... > > can anyone shed some light on this ..or point me in the right direction? > > > Thanks in advance > Zbyszek Otwinowski UT Southwestern Medical Center at Dallas 5323 Harry Hines Blvd. Dallas, TX 75390-8816 Tel. 214-645-6385 Fax. 214-645-6353 Zbyszek Otwinowski UT Southwestern Medical Center at Dallas 5323 Harry Hines Blvd. Dallas, TX 75390-8816 Tel. 214-645-6385 Fax. 214-645-6353
