• The Fine Print sticker sheet: pixel-art Noether, Raman, Goeppert Mayer and Yukawa stickers with props on a white A5 sheet
  • The Fine Print pixel-art physics sticker sheet on a desk
  • The Fine Print pixel-art physics sticker sheet – close-up of one sticker being peeled off
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The Fine Print SheetNoether, Raman, Goeppert Mayer & Yukawa | 9 Pixel Art Stickers

The Fine Print Sticker Sheet – Noether, Raman, Goeppert Mayer & Yukawa | 9 Pixel Art Stickers

$19.99 USD
$19.99 USD
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White
Shape
Kiss-Cut
Size
5.83″ × 8.27″
Made
To order · shipping times
Surface
Shape
Size

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What you getA5 sheet · 9 stickers

One A5 kiss-cut sheet (5.83″ × 8.27″) on white sticker paper with 9 stickers, made to order.

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The physics

Nine stickers on one sheet: nature's terms and conditions, read out by the four physicists who found the clauses.

Noether's line is Symmetry In. Conservation Out. In 1918 Emmy Noether proved that every continuous symmetry of the laws of physics comes with a conserved quantity. Shift the clock and energy is conserved; slide everything sideways and momentum is; rotate and angular momentum is. Those are the three cans stamped CONSERVED.

Raman's line is Most Pass Free. A Few Pay A Toll. In 1928 C. V. Raman and K. S. Krishnan found that a tiny fraction of the light scattered by a liquid comes out shifted in colour, by an amount set by the molecule's own vibrations. The photon holding the PAID receipt is one of those. Raman took the 1930 Nobel Prize alone.

Goeppert Mayer's line is A Full Floor Is Magic. Nuclei with 2, 8, 20, 28, 50, 82 or 126 protons or neutrons are unusually stable. In 1949 Maria Goeppert Mayer explained the whole list with a strong coupling between each nucleon's spin and its orbit, and Haxel, Jensen and Suess did the same independently. The dance card carries all seven.

Yukawa's line is Heavy Ball. Short Game. In 1935 Hideki Yukawa proposed that nucleons interact by exchanging a heavy particle: the heavier it is, the shorter the force's reach. He estimated about 200 electron masses. The charged pion, found in 1947, weighs about 273.

Four faces. Four clauses. Read before peeling.

Equations

\[\begin{gathered} Q = \sum_i \frac{\partial L}{\partial \dot q_i}\,\delta q_i \\ \delta L = 0 \;\Rightarrow\; \frac{dQ}{dt} = 0 \end{gathered}\]
\[\begin{gathered} h\nu_s = h\nu_0 \mp h\nu_{\text{vib}} \\ (\text{Stokes, anti-Stokes}) \end{gathered}\]
\[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ g_N = (N+1)(N+2) \end{gathered}\]
\[\begin{gathered} V_{\ell s} = -C(r)\,\vec\ell\cdot\vec s \\ \Rightarrow\; \text{magic numbers} \\ 2,\,8,\,20,\,28,\,50,\,82,\,126 \end{gathered}\]
\[\begin{gathered} V(r) = -\frac{g^{2}}{4\pi}\,\frac{e^{-r/R}}{r} \\ R = \frac{\hbar}{m c} \end{gathered}\]
SymbolMeaningUnit
\(Q\) conserved Noether charge (momentum for a shift, angular momentum for a rotation) \(\mathrm{kg·m/s, J·s}\)
\(L\) Lagrangian \(\mathrm{J}\)
\(q_i, \dot q_i\) generalised coordinates and velocities \(\mathrm{m, m/s}\)
\(\delta q_i\) direction of the symmetry shift \(\mathrm{1}\)
\(\delta L\) change in the Lagrangian under the shift \(\mathrm{J}\)
\(h\) Planck constant \(\mathrm{J·s}\)
\(\nu_0, \nu_s\) frequencies of incident and scattered light \(\mathrm{Hz}\)
\(\nu_{\text{vib}}\) molecular vibration frequency \(\mathrm{Hz}\)
\(E_N\) energy of oscillator shell N \(\mathrm{J}\)
\(N\) oscillator shell number \(\mathrm{1}\)
\(\hbar\omega\) oscillator level spacing \(\mathrm{J}\)
\(g_N\) states in shell N per nucleon species (spin included) \(\mathrm{1}\)
\(V_{\ell s}\) spin–orbit potential \(\mathrm{J}\)
\(C(r)\) radial strength of the spin–orbit term (with angular momenta in units of ħ) \(\mathrm{J}\)
\(\vec\ell, \vec s\) orbital and spin angular momentum, in units of ħ \(\mathrm{1}\)
\(V(r)\) potential energy between two nucleons \(\mathrm{J}\)
\(g\) coupling strength (g²/4π has units of energy times length) \(\mathrm{J^{1/2}·m^{1/2}}\)
\(r, R\) separation, range of the force \(\mathrm{m}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(m, c\) mass of the exchanged particle, speed of light \(\mathrm{kg, m/s}\)

Sources

  1. Noether (1918) Invariante Variationsprobleme; English translation by M. A. Tavel
  2. MacTutor — Emmy Noether biography
  3. Raman & Krishnan (1928) A New Type of Secondary Radiation, Nature 121, 501
  4. NobelPrize.org — The Nobel Prize in Physics 1930, C. V. Raman (facts)
  5. American Chemical Society — The Raman Effect, National Historic Chemical Landmark
  6. Goeppert Mayer (1949) On Closed Shells in Nuclei. II, Phys. Rev. 75, 1969
  7. Haxel, Jensen & Suess (1949) On the "Magic Numbers" in Nuclear Structure, Phys. Rev. 75, 1766
  8. NobelPrize.org — The Nobel Prize in Physics 1963 (summary)
  9. Yukawa (1935) On the Interaction of Elementary Particles. I, Proc. Phys.-Math. Soc. Japan 17, 48
  10. NobelPrize.org — Hideki Yukawa, Physics 1949 (facts)
  11. Lattes, Muirhead, Occhialini & Powell (1947) Processes involving charged mesons, Nature 159, 694
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