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Satyendra Nath Bose Sticker

Particle Guy. Major Stats. | Physics

\[\bar n(\varepsilon) = \frac{1}{e^{(\varepsilon-\mu)/(k_B T)} - 1}\]
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One short paper, and a whole family of particles took his name. In 1924 S. N. Bose derived Planck’s law by treating photons as indistinguishable; Einstein extended it. Bosons bear his name. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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The physics

Bose counted photons as truly identical particles and recovered Planck's law. The resulting Bose–Einstein distribution gives the average number of particles in a state of given energy, and it allows many bosons to pile into the same state.

The sticker says Particle Guy. Major Stats. Satyendra Nath Bose changed physics by counting differently.

In 1924 Bose, then teaching at the University of Dacca, derived Planck's radiation law without the classical electrodynamics Planck had leaned on. He treated light as a gas of quanta and counted the ways of sharing them among states, with one change: two photons in the same state are not two different objects that could trade places. Swapping them gives nothing new. He sent it to Einstein, who translated it into German himself, had it published in Zeitschrift für Physik, and then extended the counting to atoms.

Put two particles into two boxes. If the particles are distinguishable there are four arrangements: both left, both right, and two different ways of having one in each. The chance they share a box is one half. If they are identical in Bose's sense, "one in each" is a single arrangement, so there are three, and the chance they share a box rises to two thirds. Identical particles of this kind tend to bunch.

The formula on this page is the same rule at scale: the average number of particles in a state of energy ε. As ε approaches the chemical potential μ, the denominator heads to zero and the occupation grows without limit. Einstein predicted that a cold enough gas of such atoms would pile into its lowest state. In 1995 two groups did it, one with rubidium atoms in Colorado and one with sodium atoms at MIT, and the 2001 Nobel Prize followed.

Paul Dirac later named every particle that obeys Bose's counting a boson. Photons, gluons, the W and Z, the Higgs and whole helium-4 atoms are bosons. Electrons, protons and neutrons are not.

Every boson carries his name. None can tell itself from another.

Equations

\[\bar n(\varepsilon) = \frac{1}{e^{(\varepsilon-\mu)/(k_B T)} - 1}\]
Symbols
SymbolMeaningUnit
\(\bar n\) mean occupation of a single-particle state \(\mathrm{1}\)
\(\varepsilon\) state energy \(\mathrm{J}\)
\(\mu\) chemical potential \(\mathrm{J}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(T\) temperature \(\mathrm{K}\)

Source Bose, S. N. (1924). Plancks Gesetz und Lichtquantenhypothese. Zeitschrift für Physik 26, 178–181.doi.org/10.1007/BF01327326 (opens in a new tab)