• Enrico Fermi Fermi–Dirac pixel-art physics sticker, 3" × 3" / White

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Enrico Fermi Sticker

Within An Order | Physics

\[f(E)=\frac{1}{e^{(E-\mu)/kT}+1}\]
$4.99 USD
$4.99 USD
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How many piano tuners work in Chicago? Enrico Fermi loved questions like that, answered to within a power of ten. He also worked out, in 1926 alongside Dirac, how identical fermions such as electrons fill energy levels. In the Fermi–Dirac distribution, a state at the chemical potential μ is exactly half occupied at any temperature. A 3" pixel-art physicist sticker; equation, symbols and sources in the physics panel below.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

The Fermi–Dirac distribution gives the chance that a state of energy E is occupied by a fermion. Deep below the chemical potential states are full, far above it they are empty, and exactly at it the chance is one half.

Enrico Fermi estimated anything to within an order of magnitude — and co-wrote the statistics of fermions.

The Fermi–Dirac occupation is f(E)=1/(e^{(E−μ)/kT}+1). Exactly at E=μ the occupation is 1/2 for any T>0. Cold fermions fill states below μ and empty those above.

On the sticker Fermi stands at a chalkboard of decade cards (10², 10³, 10⁶…). A chalk stub, a tiny CP-1 pile in the corner, and the habit: get the power of ten right.

Fermi estimation and Fermi–Dirac statistics share one name for a reason: count the states, then occupy them.

Within an order.

Equations

\[f(E)=\frac{1}{e^{(E-\mu)/kT}+1}\]
\[f(\mu)=\tfrac12\quad(T>0)\]
SymbolMeaningUnit
\(f(E)\) Fermi–Dirac occupation probability —
\(E\) single-particle energy \(\mathrm{J}\)
\(\mu\) chemical potential \(\mathrm{J}\)
\(k\) Boltzmann constant \(\mathrm{J/K}\)
\(T\) temperature \(\mathrm{K}\)

Sources

  1. Fermi (1926) Zur Quantelung des idealen einatomigen Gases, Z. Phys. 36, 902
  2. Dirac (1926) On the theory of quantum mechanics, Proc. R. Soc. Lond. A 112, 661
  3. Pathria & Beale, Statistical Mechanics, Ch. on Fermi–Dirac statistics
  4. Mahajan, Order of Magnitude Physics (Caltech notes)

Source Fermi, E. (1926). Zur Quantelung des idealen einatomigen Gases. Zeitschrift für Physik 36, 902–912.doi.org/10.1007/bf01400221

Field notes

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