This experiment was a truly spectacular demonstration of an interference
effect, with wavelength given quantitatively by h/p. There were many more to
come! Actually, at the same time as D+G, G.P. Thomson (J.J's son) did similar
experiments with foils, more like a classic optical transmission grating.
Thomson's electrons were about 100 times more energetic, so had much smaller
wavelengths. (around 0.1 A instead of 1 A, since
.
The experiment was just like an optics experiment where you shine light through
samples, and see rings coming from diffraction around small circular objects.
These wavelengths match X-rays quite closely, and indeed, the intensity
patterns for electrons and X-rays match up nicely. One again, de Broglies
formula worked quantitatively, and a manifestly wave like property was
observed. J.J. had demonstrated that electrons were particles, and his son
showed they are waves too!
There are many more experiments one can do. E.g., you can diffract electrons around a sharp edge, or let them go through slits, and you will observe patterns just like photons. (Although the scale is quite different! Typically, wavelengths of electrons are much smaller than those for photons) The practical difficulties include making such small slits, and lensing the electrons in order to magnify the tiny distances between the resulting lines. The real classic 2-slit electron experiment, analogous to Young's (like Feynman talked about in the video) wasn't done until 1961.
Even more exciting, you can diffract not just electrons, but whole atoms. The implication is that this wave like behavior is not just a freaky property of electrons! The classic such experiment involves a beam of neutral helium atoms, bouncing/scattering off a crystal.
Once again, we expect wavelength = h/p, and one should see intense reflection of helium only in specific directions, given by the spacing of atoms in the crystal.
The geometry here is simpler than electron scattering, it's a pure "reflection grating", because helium atoms won't penetrate into the surface, so it is really a 2-D grid you're scattering from. In 1930 this experiment was performed, and agreed with de Broglie's prediction to better than 1%. The wave nature of matter is inescapable!
And still more experiments: One can now do the same thing with neutrons. This turns out to be very useful as a tool, because neutrons are neutral and very penetrating. So, the grid they see is more like what X-rays see. You can even tune their energies so their wavelength is just that same as X-rays. The key, then, is that neutrons respond to nuclei (and nuclear spin orientation), while X-rays respond primarily to electron charges. So, although the diffraction maxima are at the same places for n's and gamma's (because the grid spacing is the same), the relative intensities differ, leading to much different info about the crystal.
Going to higher energies, one can turn the wavelength down until it's not an atomic size, but a nuclear size, and then they will start to diffract off the nuclear disk! In this way, we have learned the size and composition of nuclei themselves. One can again choose the probe (electron, neutron, proton, alpha, X-ray...) to learn about different aspects and details of the target...
A brief discussion of duality, and interpretation. (see notes, syllabus section 1, page 21)
Think again of a double slit experiment.
The pattern makes total sense when we think of classical waves interfering from the 2 source slits. But, if you turn the intensity down, this pattern persists. It just becomes statistical, you have to run for a long time, the flashes come 1 by one (more often at the high points on the graph).
If you close either slit, even alternating, the pattern would vanish. Does this mean that photons split up and go through both slits? No, because if they split and divided their energy, then their wavelength would change, and the pattern should expand (but it doesn't). To understand this, we must still think of interfering amplitudes coming from both slits, but clearly can't think of these amplitudes as physical waves. They are quantum amplitudes, that have to do with probability of detection, but are not in fact that probability. (Prob = |A|^2, not A)
To finish this up, let's just review the math of 2-slit interference.
We must add two waves of equal amplitude A, whose phases differ by
.
The notes from earlier in this section give the resultant amplitude at position
y,
.
From the picture ,
,
giving
and the intensity is
.
The average intensity is 2 I_0, which is what you'd expect from two slits, putting out I_0 each.
In the limit of low intensity, this pattern represents the probability of arrival of photons.
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