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Allowed Values Only Sticker Sheet

Bifurcor, Revolvix, Stairohm & Expulsieur | 9 Pixel Art s

\[\begin{gathered} F_z = \mu_z\,\frac{\partial B_z}{\partial z} \\ \begin{gathered} \mu_z = -g_s\,\mu_B\,m_s \\ m_s = \pm\tfrac{1}{2} \end{gathered} \end{gathered}\]
$19.99 USD
$19.99 USD
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The Allowed Values Only sticker sheet gathers several Pixelated Physics characters on one page, each built on a real piece of physics. Nine kiss-cut pixel-art stickers on one A5 sheet: Bifurcor (spin ±½), Revolvix (4π), Stairohm (quantum Hall), Expulsieur (Meissner), plus props. Peel them off one at a time and stick them wherever the physics belongs.

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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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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

Stickers about quantization: Stern–Gerlach's two beams, the spin-½ sign flip under a full rotation, the exact steps of the quantum Hall resistance, and the Meissner expulsion of magnetic field from a superconductor.

Nine stickers on one sheet: four characters who will only take certain answers, filed by the Department of Quantization.

Bifurcor’s line is Two Lanes. No Middle Lane. In 1922 Otto Stern and Walther Gerlach sent silver atoms through a non-uniform magnetic field and got two separate spots, not the smear a classical magnet pointing any which way would give. The spin of the outer electron along the field comes in two values, m_s = ±½. That is the screen with two dots.

Revolvix’s line is One Turn Isn’t Enough for Me. Turn a spin-½ state through a full 360° and it comes back multiplied by −1; only 720°, or 4π, restores it. The sign shows up only against another path, and in 1975 neutron interferometers in Vienna and at the University of Missouri saw it. That is the 4π ring.

Stairohm’s line is Exact Steps. Dirt Helps. In 1980 Klaus von Klitzing found that a cold two-dimensional electron gas in a strong field has Hall resistance locked to h/(νe²) on flat plateaus. The plateaus need some disorder to be wide, and they are now how the ohm is defined. That is the staircase marked h/e².

Expulsieur’s line is Your Field Waits Outside. In 1933 Walther Meissner and Robert Ochsenfeld showed that a superconductor cooled below its transition pushes magnetic field out of its bulk, B = 0 inside except a thin surface layer. That is the cold puck and the magnet held above it. (Real levitation over most practical superconductors also relies on flux pinning; the B = 0 interior is the Meissner part.)

Equations

\[\begin{gathered} F_z = \mu_z\,\frac{\partial B_z}{\partial z} \\ \begin{gathered} \mu_z = -g_s\,\mu_B\,m_s \\ m_s = \pm\tfrac{1}{2} \end{gathered} \end{gathered}\]
\[\begin{gathered} \begin{aligned} R(2\pi)\,\psi &= e^{-i\,2\pi\,\hat{n}\cdot\boldsymbol{\sigma}/2}\,\psi \\ &= -\psi \end{aligned} \\ R(4\pi)\,\psi = +\psi \end{gathered}\]
\[\begin{gathered} \begin{gathered} R_{xy} = \frac{h}{\nu e^2} = \frac{R_K}{\nu} \\ \nu = 1, 2, 3, \ldots \end{gathered} \\ \begin{aligned} R_K &= \frac{h}{e^2} \\ &= 25\,812.807\,45\ldots\ \Omega \end{aligned} \end{gathered}\]
\[\begin{gathered} \mathbf{B}_{\text{inside}} = 0 \end{gathered}\]
SymbolMeaningUnit
\(F_z\) force on the atom along the field gradient \(\mathrm{N}\)
\(\mu_z\) z-component of the atom's magnetic moment (for silver, set by its one outer electron) \(\mathrm{J/T}\)
\(B_z\) z-component of the magnetic field \(\mathrm{T}\)
\(z\) position along the gradient, up the page \(\mathrm{m}\)
\(g_s\) electron spin g-factor, about 2.0023 \(\mathrm{1}\)
\(\mu_B\) Bohr magneton \(\mathrm{J/T}\)
\(m_s\) spin projection quantum number: only +1/2 or −1/2 \(\mathrm{1}\)
\(R(\theta)\) operator that rotates a spin-1/2 state by angle θ about the axis n \(\mathrm{1}\)
\(\psi\) two-component spinor state of a spin-1/2 particle \(\mathrm{1}\)
\(\hat{n}\) unit vector along the rotation axis \(\mathrm{1}\)
\(\boldsymbol{\sigma}\) the three Pauli matrices (σx, σy, σz) \(\mathrm{1}\)
\(2\pi, 4\pi\) one full turn (360°) and two full turns (720°) \(\mathrm{rad}\)
\(R_{xy}\) Hall resistance: transverse voltage divided by current \(\mathrm{Ω}\)
\(h\) Planck constant (exact in the SI since 2019) \(\mathrm{J·s}\)
\(e\) elementary charge (exact in the SI since 2019) \(\mathrm{C}\)
\(\nu\) filling factor: an integer on each plateau \(\mathrm{1}\)
\(R_K\) von Klitzing constant, h/e² \(\mathrm{Ω}\)
\(\mathbf{B}_{\text{inside}}\) magnetic field in the bulk of the superconductor (applied field below the critical field) \(\mathrm{T}\)

Sources

  1. Gerlach & Stern (1922) Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld, Z. Phys. 9, 349–352
  2. Friedrich & Herschbach (2003) Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics, Physics Today 56(12), 53
  3. Rauch et al. (1975) Verification of coherent spinor rotation of fermions, Phys. Lett. A 54, 425
  4. Werner, Colella, Overhauser & Eagen (1975) Observation of the Phase Shift of a Neutron Due to Precession in a Magnetic Field, Phys. Rev. Lett. 35, 1053
  5. von Klitzing, Dorda & Pepper (1980) New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Phys. Rev. Lett. 45, 494
  6. Laughlin (1981) Quantized Hall conductivity in two dimensions, Phys. Rev. B 23, 5632
  7. Meissner & Ochsenfeld (1933) Ein neuer Effekt bei Eintritt der Supraleitfähigkeit, Naturwissenschaften 21, 787 (tin and lead cylinders, field about 5 gauss)
  8. F. London & H. London (1935) The electromagnetic equations of the supraconductor, Proc. R. Soc. A 149, 71

Source Gerlach, W.; Stern, O. (1922). Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld. Zeitschrift für Physik 9, 349–352.doi.org/10.1007/BF01326983

Field notes

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