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This song is about a critical advance in our understanding of electron conduction in solids. The classical theory was developed by Paul Drude in 1900, and assumes that electrons behave like a gas, with a random thermal velocity (governed by the "Maxwell-Boltzmann distribution"), but with a small non-random component (about 0.1 mm per second) associated with the flow of electricity. Drude assumed that the electrons could be accelerated by an applied voltage until they collided with one of the atomic nuclei in the crystal lattice.

This theory was remarkably successful, and gave the correct prediction for the surprisingly small non-random "drift velocity" associated with the flow of electricity. But Drude was wrong about two key elements: thanks to the work of Enrico Fermi, we now understand that the random velocity is determined by the quantum-mechanical Pauli exclusion principle, and is much higher than the thermal velocity. (In fact, it is about two million miles per hour!) With this realization, it became clear that in fact the electrons don’t collide with the nuclei that are part of the crystal lattice, but instead collide only with crystal defects or with nuclei that have been displaced by thermal vibrations.

The modern field of solid state physics is based entirely on Fermi’s ideas of how the exclusion principle determines the distribution of occupied quantum states. However, the picture of electron behavior that many working physicists still use is the one originally developed by Drude, with the substitution of the “Fermi velocity” for the thermal velocity, and with electrons in “Bloch” quantum states which avoid collisions with the nuclei in the lattice.

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