words by Dr. James D. Livingston

tune: Yesterday, by Paul McCartney
(This was originally on the US "Yesterday and Today" album, which is no longer easily available. However, it also appears on the UK edition of "Help", which you can buy here.)
Click here to play tune

Yesterday - when old classical ideas held sway
Drude and Maxwell-Boltzmann had their say
And we believed them yesterday

Suddenly - quantum free-electron theory
Introduced the Fermi energy
And yesterday was history

Fer-mi theory you'll agree has much to say
We see Drude was wrong - he belongs to yesterday

Density - of electron states provides the key
Multiplied by probability
Reveals electron properties
Yesterday is history


Enrico Fermi


Learn more about some of the topics mentioned:
Drude Theory, Fermi energy, The interesting story of how McCartney wrote "Yesterday", Another amusing set of words for this tune

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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