The unreasonable clarity of E. M. Purcell

Edward Purcell was one of the great physicists of the 20th century.  He won the Nobel Prize in physics for his (independent) discovery of nuclear magnetic resonance, and was justifiably known for the extraordinarily clarity of his writing.  He went on to author the incredibly good second volume of the Berkeley Physics Course (soon to be re-issued in updated form by Cambridge University Press), and late in life became interested in biophysics, writing the evocative "Life at Low Reynolds Number" (pdf).   

Purcell is also known for the Purcell Factor, a really neat bit of physics.  As I mentioned previously, Einstein showed through a brilliant thermodynamic argument that it's possible to infer the spontaneous transition rate for an emitter in an excited state dropping down to the ground state and spitting out a photon.  The spontaneous emission rate is related to the stimulated rate and the absorption rate.  Both of the latter two may be calculated using "Fermi's Golden Rule", which explains (with some specific caveats that I won't list here) that the rate of a quantum mechanical radiative transition for electrons (for example) is proportional to (among other things) the density of states (number of states per unit energy per unit volume) of the electrons and the density of states of the photons.  The density of states for photons in 3d can be calculated readily, and is quadratic in frequency.  

Purcell had the insight that in a cavity, the number of states available for photons is not quadratic in frequency anymore.  Instead, a cavity on resonance has a photon density of states that is proportional to the "quality factor", Q,  of the cavity, and inversely proportional to the size of the cavity.  The better the cavity and the smaller the cavity, the higher the density of states at the cavity resonance frequency, and off-resonance the photon density of states approaches zero.  This means that the spontaneous emission rate of atoms, a property that seems like it should be fundamental, can actually be tuned by the local environment of the radiating system.  The Purcell factor is the ratio of the spontaneous emission rate with the cavity to that in free space.

While I was doing some writing today, I decided to look up the original citation for this idea.  Remarkably, the "paper" turned out to be just an abstract!  See here, page 681, abstract B10.  That one paragraph explains the essential result better than most textbooks, and it's been cited a couple of thousand times.  This takes over as my new favorite piece of clear, brief physics writing by a famous scientist, displacing my long-time favorite, Nyquist's derivation of thermal noise.  Anyone who can be both an outstanding scientist and a clear writer gets bonus points in my view.