 The very name of quantum mechanics comes from the discrete packets, the quanta that Planck, Einstein, and Bohr invented. The discrete energies that light comes in, the discrete angular momentum that electrons can have around their nucleus. But the 1920s saw a transition and understand that went from that old quantum theory to the modern version of quantum mechanics, which is still actually a precisely accurate single particle special case of quantum field theory. And quantum field theory is our current best theory of the entire contents of our universe, which survives every quantitative test that we've done. And that transition started with a French PhD student called Louis de Blois. So in the 1920s, people had somehow accepted that light was both an electromagnetic wave and that it also came in discrete energy packets. And those packets of energy had an energy that was proportional to their frequency. And if you know the energy of something that doesn't have any mass, then you also know it's momentum. And it's just equal to the Planck constant divided by the wavelength. Whereas electrons, like all matter, clearly comes in discrete packets of energy momentum, but electrons had an unexplained tendency to have quantized angular momentum when trapped around nuclei. In 1924, Louis de Blois solved this problem by doing the exact opposite of what Einstein did. Instead of taking something that everyone thought of as a wave and showing that it came in discrete quantities, he took something that everyone thought of as a discrete quantity, the electron, and described it as a wave. And he used the exact same relationship between momentum and wavelength that photons have. So these so-called matter waves were the new model for all of matter. Now that means that our electron here is not in fact a little billiard ball travelling around in a circle. What it is is some kind of wave. And this wave has a particular wavelength, and it's not exactly travelling around at just one position, but like all waves, it's spread out all over the place. But it does have to be well-defined at each point. If it's going around in a circle, then by the time it gets around the circle, this point here has to be the same as that point there. In other words, it's got to match up. And that means it has to be an integer number of wavelengths around the circle. The length around the circle is 2 pi times the radius. And that means if we use de Bois' relationship between the wavelength and the momentum, and if we rearrange this, which for a circular orbit, the momentum times the radius, it's just the angular momentum. In other words, the matter wave hypothesis explains why angular momentum is quantized. Because the wavelengths have to be standing waves around their circular orbits, you get a very discrete number of possible frequencies, just the same way as you have discrete possible frequencies for a catastrophe of a certain length. The acid test of whether something's a wave or not is of course whether you can make some kind of interference pattern or a diffraction pattern with it. In this case, the evidence came very quickly indeed. The very next year, Davison and Gauner fired some electrons at nickel and discovered a diffraction pattern. Then the year after that, Erwin Schrodinger published an equation describing exactly how that full three-dimensional wave ought to evolve. And simultaneously, Heisenberg developed a theory which turned out to be exactly the same theory in a different mathematical formulaism, and the modern theory of quantum mechanics was finally born.