An Attempt to Test the Quantum Theory of X-Ray Scattering

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We were thus looking for a new method that can provide a direct image of the quantum mechanical state straight for the experiment. Maurits Haverkort and I realized that inelastic x-ray scattering could provide such an opportunity. Using X-rays and large momentum transfers, the researchers were able to observe atomic transitions in the sample that would otherwise be forbidden in standard experiments, such as x-ray or optical absorption spectroscopy. Haverkort and Tjeng realized that by making a transition from a spherical atomic state e.

After some efforts, we were indeed able to observe the signal and the results that we had envisioned. In their experiment, Tjeng ad his colleagues used synchrotron radiation as an 'undulator' beamline, to deliver monochromatic x-rays with high intensities. They directed the x-ray beam at a sample, specifically a single crystal ; then they detected and analyzed the scattered x-rays.

The dawn of X‐ray spectroscopy - Gerward - - X-Ray Spectrometry - Wiley Online Library

In their study, Tjeng and his colleagues were able to demonstrate the effectiveness, both in terms of power and accuracy, of the imaging technique proposed by them. This is especially important for the design of new materials with new or optimized properties, which is highly desired by both the physics and chemistry research communities. Tjeng and his colleagues have presented a tangible and efficient alternative to current methods for studying orbitals in quantum materials , which could ultimately enhance research in both physics and chemistry.

In their future work, they plan to use their technique to study other complex materials. In addition, they would like to improve the apparatus and instruments employed by their method, so that it can become a standard source of measurement, such as single crystal x-ray or neutron diffraction measurement.

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Home Physics Quantum Physics. He simply took the contradiction as something which would probably be understood only much later. In the meantime the experiments of Becquerel, Curie and Rutherford had led to some clarification concerning the structure of the atom. In Rutherford's observations on the interaction of a-rays penetrating through matter resulted in his famous atomic model. The atom is pictured as consisting of a nucleus, which is positively charged and contains nearly the total mass of the atom, and electrons, which circle around the nucleus like the planets circle around the sun.

The chemical bond between atoms of different elements is explained as an interaction between the outer electrons of the neighbouring atoms; it has not directly to do with the atomic nucleus. The nucleus determines the chemical behaviour of the atom through its charge which in turn fixes the number of electrons in the neutral atom. Initially this model of the atom could not explain the most characteristic feature of the atom, its enormous stability.

The failure of classical physics and the advent of quantum mechanics

No planetary system following the laws of Newton's mechanics would ever go back to its original configuration after a collision with another such system. But an atom of the element carbon, for instance, will still remain a carbon atom after any collision or interaction in chemical binding. The explanation for this unusual stability was given by Bohr in , through the application of Planck's quantum hypothesis.

If the atom can change its energy only by discrete energy quanta, this must mean that the atom can exist only in discrete stationary states, the lowest of which is the normal state of the atom. Therefore, after any kind of interaction the atom will finally always fall back into its normal state. By this application of quantum theory to the atomic model, Bohr could not only explain the stability of the atom but also. His theory rested upon a combination of classical mechanics for the motion of the electrons with quantum conditions, which were imposed upon the classical motions for defining the discrete stationary states of the system.

A consistent mathematical formulation for those conditions was later given by Sommerfeld. Bohr was well aware of the fact that the quantum conditions spoil in some way the consistency of Newtonian mechanics.

The Interpretations of Quantum Mechanics

In the simple case of the hydrogen atom one could calculate from Bohr's theory the frequencies of the light emitted by the atom, and the agreement with the observations was perfect. Yet these frequencies were different from the orbital frequencies and their harmonies of the electrons circling around the nucleus, and this fact showed at once that the theory was still full of contradictions. But it contained an essential part of the truth.

It did explain qualitatively the chemical behaviour of the atoms and their line spectra; the existence of the discrete stationary states was verified by the experiments of Franck and Hertz, Stern and Gerlach. Bohr's theory had opened up a new line of research. The great amount of experimental material collected by spectroscopy through several decades was now available for information about the strange quantum laws governing the motions of the electrons in the atom.

The many experiments of chemistry could be used for the same purpose. It was from this time on that the physicists learned to ask the right questions; and asking the right question is frequently more than halfway to the solution of the problem. What were these questions?

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Practically all of them had to do with the strange apparent contradictions between the results of different experiments. How could it be that the same radiation that produces interference patterns, and therefore must consist of waves, also produces the photoelectric effect, and therefore must consist of moving particles? How could it be that the frequency of the orbital motion of the electron in the atom does not show up in the frequency of the emitted radiation? Does this mean that there is no orbital motion? But if the idea of orbital motion should be incorrect, what happens to the electrons inside the atom?

One can see the electrons move through a cloud chamber, and sometimes they are knocked out of an atom- why should they not also move within the atom? It is true that they might be at rest in the normal state of the atom, the state of lowest energy. But there are many states of higher energy, where the electronic shell has an angular momentum. There the electrons cannot possibly be at rest. One could add a number of similar examples.

Our quantum problem

Again and again one found that the attempt to describe atomic events in the traditional terms of physics led to contradictions. Gradually, during the early twenties, the physicists became accustomed to these difficulties, they acquired a certain vague knowledge about where trouble would occur, and they learned to avoid contradictions. They knew which description of an atomic event would be the correct one for the special experiment under discussion. This was not sufficient to form a consistent general picture of what happens in a quantum process, but it changed the minds of the physicists in such a way that they somehow got into the spirit of quantum theory.

Therefore, even some time before one had a consistent formulation of quantum theory one knew more or less what would be the result of any experiment. One frequently discussed what one called ideal experiments. Such experiments were designed to answer a very critical question irrespective of whether or not they could actually be carried out. Of course it was important that it should be possible in principle to carry out the experiment, but the technique might be extremely complicated.

These ideal experiments could be very useful in clarifying certain problems. If there was no agreement among the physicists about the result of such an ideal experiment, it was frequently possible to find a similar but simpler experiment that could be carried out, so that the experimental answer contributed essentially to the clarification of quantum theory.


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The strangest experience of those years was that the paradoxes of quantum theory did not disappear during this process of clarification; on the contrary, they became even more marked and more exciting. There was, for instance, the experiment of Compton on the scattering of X-rays. From earlier experiments on the interference of scattered light there could be no doubt that scattering takes place essentially in the following way: The incident light wave makes an electron in the beam vibrate in the frequency of the wave; the oscillating electron then emits a spherical wave with the same frequency and thereby produces the scattered light.