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目录中的所有方程，每件商品一行。

  1. Airy Disk Hoodie – EVEN A PERFECT LENS BLURS | Pixelated PhysicsHoodie \[I(x) = I_0\left(\frac{2J_1(x)}{x}\right)^2,\qquad x = \frac{\pi D\sin\theta}{\lambda}\]\[\sin\theta_1 = 1.22\,\frac{\lambda}{D}\]
  2. Allowed Values Only Sticker Sheet – Bifurcor, Revolvix, Stairohm & Expulsieur | 9 Pixel Art StickersPaper products \[\begin{gathered} F_z = \mu_z\,\frac{\partial B_z}{\partial z} \\ \begin{gathered} \mu_z = -g_s\,\mu_B\,m_s \\ m_s = \pm\tfrac{1}{2} \end{gathered} \end{gathered}\]\[\begin{gathered} \begin{aligned} R(2\pi)\,\psi &= e^{-i\,2\pi\,\hat{n}\cdot\boldsymbol{\sigma}/2}\,\psi \\ &= -\psi \end{aligned} \\ R(4\pi)\,\psi = +\psi \end{gathered}\]\[\begin{gathered} \begin{gathered} R_{xy} = \frac{h}{\nu e^2} = \frac{R_K}{\nu} \\ \nu = 1, 2, 3, \ldots \end{gathered} \\ \begin{aligned} R_K &= \frac{h}{e^2} \\ &= 25\,812.807\,45\ldots\ \Omega \end{aligned} \end{gathered}\]\[\begin{gathered} \mathbf{B}_{\text{inside}} = 0 \end{gathered}\]
  3. Arnold's Cat – Cat Map Chaos Physics T-ShirtT-Shirt \[\Gamma:\ (x, y) \mapsto (x + y,\ x + 2y) \bmod 1\]\[A = \begin{pmatrix}1 & 1\\ 1 & 2\end{pmatrix},\quad \det A = 1,\quad \lambda_\pm = \frac{3 \pm \sqrt{5}}{2}\]\[\Pi(124) = 15\]
  4. Azurwake – Cherenkov Radiation / Light-Speed in Water Physics StickerPaper products \[\cos\theta = \frac{1}{n\beta}, \qquad \beta > \frac{1}{n}\]\[\begin{aligned} \frac{d^2N}{dx\,d\lambda} &= \frac{2\pi\alpha z^2}{\lambda^2} \\ &\quad\times\left(1-\frac{1}{\beta^2 n^2}\right) \end{aligned}\]
  5. Beats Hoodie – TWO CLOSE NOTES PULSE | Pixelated PhysicsHoodie \[x = \cos(2\pi f_1 t)+\cos(2\pi f_2 t) = 2\cos(\pi\Delta f\, t)\cos(2\pi\bar f\, t)\]\[\Delta f = |f_1-f_2|,\quad \bar f=(f_1+f_2)/2\]
  6. Bernoulla – Bernoulli’s Principle Physics MugMug \[P + \tfrac{1}{2}\rho v^{2} + \rho g h = \text{const}\]
  7. Bifurcation Hoodie – SPLIT, SPLIT, SPLIT, CHAOS | Pixelated PhysicsHoodie \[x_{n+1} = r\,x_n(1-x_n)\]\[\delta = \lim_{k\to\infty}\frac{r_k - r_{k-1}}{r_{k+1}-r_k} = 4.6692\ldots\]
  8. Bifurcor – Stern–Gerlach Experiment / Spin Quantization Physics StickerPaper products \[F_z = \mu_z\,\frac{\partial B_z}{\partial z}\]\[\begin{gathered} \mu_z = -g_s\,\mu_B\,m_s \\ m_s = \pm\tfrac{1}{2} \end{gathered}\]
  9. Blackbody Hoodie – THE CURVES NEVER CROSS | Pixelated PhysicsHoodie \[B_\lambda(T) = \frac{2hc^2}{\lambda^5}\,\frac{1}{e^{hc/\lambda k_BT} - 1}\]\[\lambda_{\max}T = 2898\ \mu\mathrm{m\,K}\]
  10. Bose-Einstein Condensate 1995 TeeT-Shirt \[\lambda_{\mathrm{dB}} = \frac{h}{\sqrt{2\pi m k_B T}}\]\[n\,\lambda_{\mathrm{dB}}^{3} = \zeta(3/2) \approx 2.612\]\[k_B T_c = \frac{2\pi\hbar^{2}}{m}\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\quad\text{(uniform gas)}\]\[k_B T_c \approx 0.94\,\hbar\bar\omega\,N^{1/3}\quad\text{(harmonic trap)}\]
  11. Boylina – Boyle’s Law Physics MugMug \[P_1V_1 = P_2V_2\]\[PV = \text{const}\quad (\text{fixed } T,\ n)\]
  12. Brachistochrone Hoodie – STRAIGHT IS NOT THE FASTEST | Pixelated PhysicsHoodie \[x = R(\theta - \sin\theta),\qquad y = R(1 - \cos\theta)\]\[\theta = t\sqrt{g/R}\]\[T_{\text{cycloid}} = \pi\sqrt{R/g},\qquad T_{\text{straight}} = \sqrt{\pi^2+4}\,\sqrt{R/g}\]
  13. Bremsella – Bremsstrahlung (Braking Radiation) Physics StickerPaper products \[P = \frac{q^2 a^2}{6\pi\varepsilon_0 c^3}\]
  14. Brownian Motion Hoodie – NO STEP REMEMBERS THE LAST | Pixelated PhysicsHoodie \[\langle r^2\rangle = 4Dt\quad\text{(2D)}\]\[D = \frac{k_BT}{6\pi\eta a}\]\[m\ddot{x} = -\gamma\dot{x} + F(t)\]
  15. Buoyara – Archimedes’ Principle Physics MugMug \[F_b = \rho_{\text{fluid}}\,V\,g\]
  16. C. V. Raman Sticker – Most Pass Free. A Few Pay A Toll. | Physics StickerPaper products \[\begin{gathered} h\nu_s = h\nu_0 - h\nu_{\text{vib}} \\ (\text{Stokes}) \end{gathered}\]\[\begin{gathered} h\nu_s = h\nu_0 + h\nu_{\text{vib}} \\ (\text{anti-Stokes}) \end{gathered}\]\[\Delta\tilde\nu = \frac{1}{\lambda_0} - \frac{1}{\lambda_s}\]
  17. Casimira – Casimir Effect Physics StickerPaper products \[\frac{F}{A} = -\frac{\pi^2\hbar c}{240\,d^4}\]
  18. Catenary Hoodie – THE CHAIN FINDS THIS CURVE | Pixelated PhysicsHoodie \[y = a\cosh(x/a)\]\[T = \mu g y,\qquad V = \mu g\int y\,ds\]
  19. Caustic Hoodie – YOUR COFFEE HAS A CUSP | Pixelated PhysicsHoodie \[x = \tfrac{R}{4}\left(3\cos t-\cos 3t\right)\]\[y = \tfrac{R}{4}\left(3\sin t-\sin 3t\right),\quad -\tfrac{\pi}{2}\le t\le\tfrac{\pi}{2}\]
  20. Cecilia Payne-Gaposchkin Sticker – Almost Certainly Real. | Physics StickerPaper products \[\begin{aligned} \frac{n_{i+1}\,n_e}{n_i} &= \frac{2}{\Lambda^{3}}\,\frac{g_{i+1}}{g_i} \\ &\quad\times\exp\!\left(-\frac{\chi_i}{k_B T}\right) \\ \Lambda &= \frac{h}{\sqrt{2\pi m_e k_B T}} \end{aligned}\]\[\begin{gathered} X + Y + Z = 1 \\ (\text{Sun's surface today:} \\ X\approx0.74,\ Y\approx0.25, \\ Z\approx0.013) \end{gathered}\]
  21. Chandrasekhar Limit Tee: 1.4 M☉T-Shirt \[M_{\mathrm{Ch}} = \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2}\frac{1}{(\mu_e m_H)^{2}} \approx \frac{5.8\,M_\odot}{\mu_e^{2}}\]\[\mu_e = 2 \;\Rightarrow\; M_{\mathrm{Ch}} \approx 1.44\,M_\odot\ \text{(ideal)},\ \approx 1.4\,M_\odot\ \text{(real white dwarfs)}\]
  22. Chien-Shiung Wu Sticker – She Broke Symmetry. And Records. | Physics StickerPaper products \[{}^{60}\mathrm{Co} \to {}^{60}\mathrm{Ni}^{*} + e^{-} + \bar\nu_e\]\[\begin{gathered} \hat P:\ \vec J \to \vec J,\ \ \vec p_e \to -\vec p_e \\ \Rightarrow\; \langle \vec J\cdot\vec p_e\rangle \ne 0 \\ \text{violates parity} \end{gathered}\]
  23. Christiaan Huygens Sticker – Every Point A Source | Physics StickerPaper products \[r = v\,\Delta t\]\[\text{new front} = \text{envelope of the wavelets}\]
  24. Condensa – Bose–Einstein Condensate Physics StickerPaper products \[\frac{N_0}{N} = 1 - \left(\frac{T}{T_c}\right)^{3/2}\quad(T\le T_c)\]\[kT_c = \frac{2\pi\hbar^2}{m}\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\]
  25. Corekeeper – Strong Nuclear Force / Nuclear Binding Physics T-ShirtT-Shirt \[V(r) = -\frac{g^{2}}{4\pi}\frac{e^{-r/\lambda}}{r}, \qquad \lambda = \frac{\hbar}{m_\pi c}\]\[B = \left(Z m_p + N m_n - M_{\text{nuc}}\right)c^{2}\]
  26. Coriolix – Coriolis Effect Physics StickerPaper products \[\mathbf{a}' = -2\,\boldsymbol{\Omega}\times\mathbf{v}' - \boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\mathbf{r}')\]\[x' = vt\cos\Omega t,\qquad y' = -vt\sin\Omega t\]\[\Delta\varphi = \frac{\Omega R}{v}\]
  27. Cosmic Weights & Measures Sticker Sheet – Rømer, Payne-Gaposchkin, du Châtelet & Chandrasekhar | 9 Pixel Art StickersPaper products \[\begin{gathered} \Delta t = \frac{\Delta d}{c} \\ \frac{2\,\text{AU}}{c} \approx 16.6\ \text{min} \end{gathered}\]\[\begin{gathered} X + Y + Z = 1 \\ (\text{Sun's surface today:} \\ X\approx0.74,\ Y\approx0.25, \\ Z\approx0.013) \end{gathered}\]\[\begin{gathered} \frac{1}{\lambda_{\text{vac}}} = R_{\text{H}}\left(\frac{1}{2^{2}} - \frac{1}{n^{2}}\right) \\ n = 3,\ldots,6 \\ \Rightarrow\; \lambda_{\text{air}} \approx 656.3,\ 486.1, \\ 434.0,\ 410.2\ \text{nm} \end{gathered}\]\[\begin{gathered} E_k = \tfrac{1}{2} m v^{2} \\ v = \sqrt{2 g h}\;\Rightarrow\; h \propto v^{2} \end{gathered}\]\[\begin{gathered} M_{\text{Ch}} \approx \frac{5.73}{\mu_e^{2}}\,M_\odot \approx 1.4\,M_\odot \\ (\mu_e = 2) \end{gathered}\]
  28. Coulombo – Coulomb’s Law Physics MugMug \[F = k_e\,\frac{q_1 q_2}{r^{2}}\]\[k_e = \frac{1}{4\pi\varepsilon_0}\]\[k_e \approx 8.99\times10^{9}\ \text{N m}^{2}\,\text{C}^{-2}\]
  29. Cryo Fault – Ductile-to-Brittle Transition Physics MugMug \[K_I = Y\sigma\sqrt{\pi a} \ge K_{Ic} \;\Rightarrow\; \text{fracture}\]\[\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}\quad\text{(Griffith, plane stress)}\]
  30. Cryo Fault – Ductile-to-Brittle Transition Physics T-ShirtT-Shirt \[\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}\]\[K_I = Y\sigma\sqrt{\pi a} \ \ge\ K_{Ic} \;\Rightarrow\; \text{fracture}\]
  31. Current Affairs Sticker Sheet – Vortessa, Saltara, Pendulux & Libratrix | 9 Pixel Art StickersPaper products \[\begin{gathered} f = \mathrm{St}\,\frac{U}{D}, \qquad \mathrm{St} \approx 0.2 \end{gathered}\]\[\begin{gathered} \mathrm{Fr} = \frac{v}{\sqrt{g h}} \\ \frac{h_2}{h_1} = \frac{1}{2}\left(\sqrt{1 + 8\,\mathrm{Fr}_1^2} - 1\right) \end{gathered}\]\[\begin{gathered} \omega_{\text{prec}} = \Omega_\oplus \sin\varphi \end{gathered}\]\[\begin{gathered} r_{L2} \approx R\left(\frac{M_2}{3M_1}\right)^{1/3} \end{gathered}\]
  32. Dark Matter Host – Gravitational Lensing / Invisible Mass Physics T-ShirtT-Shirt \[v(r)^{2} = \frac{G M(r)}{r} \;\Rightarrow\; M(r) = \frac{v^{2} r}{G}\]\[\theta_E = \sqrt{\frac{4GM}{c^{2}}\,\frac{D_{LS}}{D_L D_S}}\]
  33. Dark Matter Host – Gravitational Lensing Physics MugMug \[\theta_E = \sqrt{\frac{4GM}{c^{2}}\,\frac{D_{LS}}{D_L D_S}}\]\[M(r) = \frac{v^{2} r}{G}\]
  34. Debroglio – Matter Waves Physics MugMug \[\lambda = \frac{h}{p}\]
  35. Decay Dancer – Weak Nuclear Force / Beta Decay Physics T-ShirtT-Shirt \[n \to p + e^{-} + \bar\nu_e\]\[d \to u + W^{-} \to u + e^{-} + \bar\nu_e\]\[Q = \left(m_n - m_p - m_e\right)c^{2} \approx 0.782\ \text{MeV}\]
  36. Decoherex – The Interference / Quantum Decoherence Physics T-ShirtT-Shirt \[\rho_{01}(t) = \rho_{01}(0)\,e^{-t/\tau_D}\]
  37. Diagonix – Malus’s Law / Three-Polarizer Effect Physics StickerPaper products \[I = I_0\cos^2\theta\]\[I_{\text{out}} = \frac{I_0}{2}\cos^2 45^\circ\,\cos^2 45^\circ\]\[I_{\text{out}} = \frac{I_0}{8}\]
  38. Diffraction Hoodie – SPOTS WHERE THE ROWS AGREE | Pixelated PhysicsHoodie \[n\lambda = 2d\sin\theta\]\[\mathbf{k} - \mathbf{k}_0 = \mathbf{G}\]\[I(\mathbf{q}) \propto \Big|\sum_j e^{i\mathbf{q}\cdot\mathbf{r}_j}\Big|^2\]
  39. Dilatia – Time Dilation Physics MugMug \[\Delta t = \gamma\,\Delta t_0\]\[\gamma = \frac{1}{\sqrt{1 - v^{2}/c^{2}}}\]
  40. Disordra – Entropy Physics MugMug \[S = k_B \ln \Omega\]\[\Delta S_{\text{isolated}} \ge 0\]
  41. Dopplerine – Doppler Effect Physics MugMug \[f = f_0\,\frac{v + v_o}{v - v_s}\]
  42. Double Pendulum Hoodie – TWO HINGES ARE ENOUGH | Pixelated PhysicsHoodie \[L = ml^2\left[\dot\theta_1^2 + \tfrac12\dot\theta_2^2 + \dot\theta_1\dot\theta_2\cos(\theta_1-\theta_2)\right] + mgl\left(2\cos\theta_1 + \cos\theta_2\right)\]\[\frac{d}{dt}\frac{\partial L}{\partial\dot\theta_i} = \frac{\partial L}{\partial\theta_i}\]
  43. Double Slit Hoodie – DARK WHERE THE PATHS DISAGREE | Pixelated PhysicsHoodie \[I(\theta) = I_0\cos^2\!\left(\frac{\pi d\sin\theta}{\lambda}\right)\mathrm{sinc}^2\!\left(\frac{\pi a\sin\theta}{\lambda}\right)\]\[d\sin\theta = m\lambda \;\text{(bright)}\]\[d = 4a\]
  44. Drum Mode Hoodie – SOME DRUMS SOUND IDENTICAL | Pixelated PhysicsHoodie \[\nabla^2 u = \frac{1}{c^2}\frac{\partial^2 u}{\partial t^2}\]\[u(r,\theta,t) = J_3(kr)\cos 3\theta\cos\omega t\]\[kR = j_{3,2} = 9.7610\]
  45. Einstein Ring Hoodie – ONE GALAXY, SEEN AS A RING | Pixelated PhysicsHoodie \[\beta = \theta - \frac{\theta_E^2}{\theta}\]\[\theta_E^2 = \frac{4GM}{c^2}\,\frac{D_{ls}}{D_l\,D_s}\]
  46. Émilie du Châtelet Sticker – 2× The Speed. 4× The Dent. | Physics StickerPaper products \[\begin{gathered} E_k = \tfrac{1}{2} m v^{2} \\ (\text{vis viva: } m v^{2}) \end{gathered}\]\[v = \sqrt{2 g h}\;\Rightarrow\; h \propto v^{2}\]\[\begin{gathered} m g h \approx F d\;\Rightarrow\; d \propto v^{2} \\ (\text{idealised: constant} \\ \text{clay resistance}) \end{gathered}\]\[\begin{gathered} m_1 h_1 = m_2 h_2 \\ \Leftrightarrow\; m_1 v_1^{2} = m_2 v_2^{2} \\ \Rightarrow\; \text{equal dents} \\ (\text{'s Gravesande}) \end{gathered}\]
  47. Emmy Noether Sticker – Symmetry In. Conservation Out. | Physics StickerPaper products \[Q = \sum_i \frac{\partial L}{\partial \dot q_i}\,\delta q_i\]\[\delta L = 0 \;\Rightarrow\; \frac{dQ}{dt} = 0\]\[\begin{gathered} E = \sum_i \dot q_i\,\frac{\partial L}{\partial \dot q_i} - L \\ \frac{\partial L}{\partial t} = 0 \;\Rightarrow\; \frac{dE}{dt} = 0 \end{gathered}\]\[\begin{aligned} t \to t+\epsilon \;&\Rightarrow\; E \text{ conserved} \\ \vec x \to \vec x+\vec\epsilon \;&\Rightarrow\; \vec p \\ \theta \to \theta+\epsilon \;&\Rightarrow\; \vec L \end{aligned}\]
  48. Energy Accounts Sticker Sheet – Sortex, Invertia, Vevette & Moderon | 9 Pixel Art StickersPaper products \[\begin{gathered} Q_{\text{erase}} \ge k_B T \ln 2 \end{gathered}\]\[\begin{gathered} \frac{1}{T} = \frac{\partial S}{\partial E} < 0 \end{gathered}\]\[\begin{gathered} V(\phi) = -\mu^2|\phi|^2 + \lambda|\phi|^4 \\ \begin{gathered} \langle\phi\rangle = \frac{v}{\sqrt{2}} \\ v = (\sqrt{2}\,G_F)^{-1/2} \end{gathered} \\ v \approx 246\ \text{GeV} \end{gathered}\]\[\begin{gathered} \alpha = \left(\frac{A-1}{A+1}\right)^2 \end{gathered}\]
  49. Enrico Fermi Sticker – Within An Order | Physics StickerPaper products \[f(E)=\frac{1}{e^{(E-\mu)/kT}+1}\]\[f(\mu)=\tfrac12\quad(T>0)\]
  50. Entangla & Entanglo – Quantum Entanglement Physics MugMug \[\lvert\Phi^{+}\rangle = \frac{\lvert 00\rangle + \lvert 11\rangle}{\sqrt{2}}\]\[P(00) = P(11) = \tfrac{1}{2}\]
  51. Ernest Rutherford Sticker – Some Came Back | Physics StickerPaper products \[\frac{d\sigma}{d\Omega} = \left(\frac{zZe^2}{16\pi\varepsilon_0 E}\right)^2\frac{1}{\sin^4(\theta/2)}\]\[\tan\frac{\theta}{2} = \frac{d}{2b},\qquad d = \frac{zZe^2}{4\pi\varepsilon_0 E}\]
  52. Eventide Prophet – Black Hole Information Paradox Physics MugMug \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[T_H \approx 6\times10^{-8}\ \text{K}\times\frac{M_\odot}{M}\]\[S_{BH} = \frac{k_B c^{3} A}{4 G \hbar}\]
  53. Eventide Prophet – Black Hole Information Paradox Physics T-ShirtT-Shirt \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[S_{BH} = \frac{k_B c^{3} A}{4 G \hbar}\]\[\begin{gathered} S_{\text{rad}}(t) \le S_{BH}(t) \\ \text{unitary evaporation} \\ (\text{Page 1993}) \end{gathered}\]
  54. Exclusor – Pauli Exclusion Physics MugMug \[\psi(x_1,x_2) = \tfrac{1}{\sqrt{2}}\,\bigl[\,\psi_{ab} - \psi_{ba}\,\bigr]\]\[\psi_{ab} = \phi_a(x_1)\,\phi_b(x_2)\]\[\psi(x_2,x_1) = -\,\psi(x_1,x_2)\]\[\phi_a = \phi_b \;\Rightarrow\; \psi = 0\]\[P = \frac{(3\pi^{2})^{2/3}}{5}\,\frac{\hbar^{2}}{m_e}\,n_e^{5/3}\]
  55. Exclusor – Pauli Exclusion Principle / Degeneracy Pressure Physics T-ShirtT-Shirt \[\psi(x_1,x_2) = \frac{1}{\sqrt{2}}\begin{vmatrix} \phi_a(x_1) & \phi_b(x_1) \\ \phi_a(x_2) & \phi_b(x_2) \end{vmatrix}\]\[\psi(x_2,x_1) = -\,\psi(x_1,x_2)\]\[\phi_a = \phi_b \;\Rightarrow\; \psi = 0\]\[P = \frac{(3\pi^{2})^{2/3}}{5}\,\frac{\hbar^{2}}{m_e}\,n_e^{5/3}\]
  56. Expulsieur – Meissner Effect / Flux Expulsion Physics StickerPaper products \[\mathbf{B}_{\text{inside}} = 0\]\[B(x) = B_0\,e^{-x/\lambda_L}\]\[\lambda_L = \sqrt{\frac{m}{\mu_0 n_s e^2}}\]
  57. Faradax – Faraday’s Law Physics MugMug \[\mathcal{E} = -\frac{d\Phi_B}{dt}\]\[\Phi_B = \int \vec B\cdot d\vec A\]
  58. Feynman Diagram Hoodie – TWO IN, ONE PHOTON, TWO OUT | Pixelated PhysicsHoodie \[\frac{d\sigma}{d\Omega} = \frac{\alpha^2}{4s}\left(1+\cos^2\theta\right)\]\[\sigma = \frac{4\pi\alpha^2}{3s}\quad (\hbar = c = 1,\; \sqrt{s}\gg m_\mu)\]
  59. Field Lines Hoodie – START POSITIVE | Pixelated PhysicsHoodie \[\nabla\cdot\mathbf{E} = \frac{\rho}{\varepsilon_0}\]\[\mathbf{E}(\mathbf{r}) = \sum_i \frac{k\,q_i\,(\mathbf{r}-\mathbf{r}_i)}{|\mathbf{r}-\mathbf{r}_i|^3},\qquad k = \frac{1}{4\pi\varepsilon_0}\]
  60. Field Work Sticker Sheet – Lenzor, Gyrolla, Azurwake & Diagonix | 9 Pixel Art StickersPaper products \[\begin{gathered} \mathcal{E} = -\frac{d\Phi_B}{dt} \end{gathered}\]\[\begin{gathered} q v B = \frac{m v^2}{r} \;\Rightarrow\; r = \frac{m v}{q B} \\ f_c = \frac{q B}{2\pi m} \end{gathered}\]\[\begin{gathered} \cos\theta = \frac{1}{n\beta}, \qquad \beta > \frac{1}{n} \end{gathered}\]\[\begin{gathered} I = I_0\cos^2\theta \\ I_{\text{out}} = \frac{I_0}{2}\cos^2 45^\circ\,\cos^2 45^\circ \\ I_{\text{out}} = \frac{I_0}{8} \end{gathered}\]
  61. ForceShift – Quantum Tunnelling / Barrier Penetration Physics T-ShirtT-Shirt \[T \approx e^{-2\kappa L}, \qquad \kappa = \frac{\sqrt{2m(V_0 - E)}}{\hbar}\]
  62. Foucault Hoodie – THE FLOOR TURNS UNDER ME | Pixelated PhysicsHoodie \[\Omega = \omega_\oplus\sin\phi\]\[\dot\theta = -\omega_\oplus\sin\phi,\qquad T = 2\pi/|\Omega|\]
  63. Fritz Zwicky Sticker – Too Fast To Be Lit | Physics StickerPaper products \[\sigma^2 \sim \frac{GM}{R}\]\[M_{\mathrm{vir}} \approx \frac{\sigma^2 R}{G}\]
  64. Fuzzwick – Uncertainty Principle Physics MugMug \[\sigma_x\,\sigma_p \ge \frac{\hbar}{2}\]\[\sigma_A\,\sigma_B \ge \tfrac{1}{2}\left\lvert\langle[\hat A,\hat B]\rangle\right\rvert\]\[[\hat x,\hat p] = i\hbar\]
  65. Galileo Galilei Sticker – Telescope. Tea. Trouble with the Church. | Physics StickerPaper products \[d = \tfrac{1}{2}g t^{2}\]\[d_1 : d_2 : d_3 : \dots = 1 : 3 : 5 : \dots\]
  66. Ghostwall – Quantum Tunnelling Physics MugMug \[T \approx e^{-2\kappa L}\]\[\kappa = \frac{\sqrt{2m(V_0 - E)}}{\hbar}\]
  67. Graviton Whisper – Quantum Gravity / Force Carrier Physics T-ShirtT-Shirt \[\Box\,\bar h_{\mu\nu} = -\frac{16\pi G}{c^{4}}\,T_{\mu\nu}\]\[E = hf, \qquad m_{g} = 0 \ (\text{if it exists}),\ \ s = 2\]\[m_g \le 1.27\times10^{-23}\ \mathrm{eV}/c^{2}\quad\text{(LIGO–Virgo–KAGRA, GWTC-3, 90\% credible)}\]
  68. Graviton Whisper – Quantum Gravity Physics MugMug \[E = hf\]\[m_g = 0\]\[s = 2\quad\text{(if the graviton exists)}\]
  69. Gyrolla – Cyclotron Motion / Lorentz Force Physics StickerPaper products \[q v B = \frac{m v^2}{r} \;\Rightarrow\; r = \frac{m v}{q B}\]\[f_c = \frac{q B}{2\pi m}\]\[\frac{f_c}{B} \approx 15.2\ \text{MHz/T}\ (\text{proton})\]
  70. Hadron Brawler – Strong Nuclear Force / Quantum Chromodynamics Physics T-ShirtT-Shirt \[V(r) = -\frac{4}{3}\frac{\alpha_s \hbar c}{r} + \sigma r\]
  71. Hawkara – Hawking Radiation Physics MugMug \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[T_H \approx 6\times10^{-8}\ \text{K}\times\frac{M_\odot}{M}\]
  72. Henrietta Swan Leavitt Sticker – The Blink Is the Ruler | Physics StickerPaper products \[M_V = -2.43\,(\log_{10} P - 1) - 4.05\]\[m - M = 5\log_{10}\frac{d}{10\,\mathrm{pc}}\]
  73. Hideki Yukawa Sticker – Heavy Ball. Short Game. | Physics StickerPaper products \[\begin{gathered} V(r) = -\frac{g^{2}}{4\pi}\,\frac{e^{-r/R}}{r} \\ R = \frac{\hbar}{m c} \end{gathered}\]\[\begin{aligned} R &= \frac{1}{\lambda} = 2\ \text{fm} \\ \Rightarrow\; mc^{2} &= \frac{\hbar c}{R} \approx 99\ \text{MeV} \\ &\approx 2\times10^{2}\,m_e c^{2} \end{aligned}\]
  74. Higgsby – Higgs Mechanism Physics MugMug \[m_f = \frac{y_f\,v}{\sqrt{2}}\]\[v \approx 246\ \text{GeV}\]
  75. I Twist Space Itself – Spacetime Distortion Physics T-ShirtT-Shirt \[\alpha = \frac{4GM}{c^{2}b}\]\[\alpha_{\text{Newton}} = \frac{2GM}{c^{2}b} = \tfrac{1}{2}\,\alpha\]
  76. Inertio – Newton’s Second Law Physics MugMug \[\vec F_{\text{net}} = m\,\vec a\]\[\vec F_{\text{net}} = \frac{d\vec p}{dt},\qquad \vec p = m\vec v\]
  77. Interfera – The Path Unchosen / Quantum Interference Physics T-ShirtT-Shirt \[P = \lvert\psi_1 + \psi_2\rvert^{2} = \lvert\psi_1\rvert^{2} + \lvert\psi_2\rvert^{2} + 2\,\mathrm{Re}\!\left(\psi_1^{*}\psi_2\right)\]\[\Delta y = \frac{\lambda L}{d}, \qquad \lambda = \frac{h}{p}\]
  78. Invertia – Negative Absolute Temperature / Population Inversion Physics StickerPaper products \[\frac{1}{T} = \frac{\partial S}{\partial E} < 0\]\[\frac{N_{\uparrow}}{N_{\downarrow}} = e^{-\Delta E/k_B T}\]\[T < 0 \;\Rightarrow\; N_{\uparrow} > N_{\downarrow}\]
  79. Isaac Newton Sticker – Gravity Hits Different | Physics StickerPaper products \[\vec F = \frac{d\vec p}{dt}\]\[F = \frac{G m_1 m_2}{r^{2}}\]
  80. Ising Model Hoodie – EVERY SCALE AT ONCE | Pixelated PhysicsHoodie \[H = -J\sum_{\langle ij\rangle} s_is_j,\qquad s_i = \pm1\]\[k_BT_c = \frac{2J}{\ln(1+\sqrt2)} \approx 2.269\,J\]
  81. James Clerk Maxwell Sticker – Field Goals Achieved | Physics StickerPaper products \[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}, \quad \nabla\cdot\vec B = 0\]\[\nabla\times\vec E = -\frac{\partial\vec B}{\partial t}, \quad \nabla\times\vec B = \mu_0\vec J + \mu_0\varepsilon_0\frac{\partial\vec E}{\partial t}\]\[c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\]
  82. Jocelyn Bell Burnell Sticker – She Found Pulsars. They Gave Her Silence. | Physics StickerPaper products \[\bar\rho \gtrsim \frac{3\pi}{G P^{2}}\]\[\Delta t = \frac{e^{2}}{8\pi^{2}\varepsilon_0 m_e c}\,\mathrm{DM}\left(f_1^{-2} - f_2^{-2}\right)\]
  83. Kepler Orbit Hoodie – FAST WHEN CLOSE, EXACTLY | Pixelated PhysicsHoodie \[\frac{dA}{dt} = \frac{L}{2m} = \text{const}\]\[M = E - e\sin E,\qquad M = \frac{2\pi t}{P}\]\[\tan\frac{\nu}{2} = \sqrt{\frac{1+e}{1-e}}\tan\frac{E}{2}\]
  84. Keplora – Kepler’s Third Law Physics MugMug \[T^{2} = \frac{4\pi^{2}}{GM}\,a^{3}\]
  85. Lagrange Points Hoodie – FIVE PLACES TO PARK | Pixelated PhysicsHoodie \[U = -\frac{1-\mu}{r_1} - \frac{\mu}{r_2} - \frac{x^2+y^2}{2}\]\[\nabla U = 0\;\text{at } L_1\ldots L_5\]\[\mu < \mu_c = \tfrac12\left(1-\sqrt{\tfrac{23}{27}}\right) \approx 0.0385\;\text{(}L_4, L_5\text{ stable)}\]
  86. Lenzor – Lenz’s Law / Eddy-Current Braking Physics StickerPaper products \[\mathcal{E} = -\frac{d\Phi_B}{dt}\]\[m g = F_{\text{eddy}}(v_t) \propto \sigma\,v_t\]
  87. Libratrix – Lagrange Points / Three-Body Equilibrium Physics StickerPaper products \[r_{L2} \approx R\left(\frac{M_2}{3M_1}\right)^{1/3}\]\[r_{L2} \approx 1.5\times10^{6}\ \text{km}\]\[\frac{M_1}{M_2} > \frac{25+\sqrt{621}}{2} \approx 24.96\]
  88. Light Cone Hoodie – ELSEWHERE IS A REAL PLACE | Pixelated PhysicsHoodie \[ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2\]\[ds^2 = 0\;\text{on the cone}\]\[x(t) = \frac{c^2}{g}\left(\sqrt{1+\left(\frac{gt}{c}\right)^2}-1\right)\]
  89. Lise Meitner Sticker – Split Happens | Physics StickerPaper products \[Q = \left(M_{\text{initial}} - M_{\text{final}}\right)c^{2}\]\[E_C = \frac{Z_1 Z_2 e^{2}}{4\pi\varepsilon_0\,d}\]
  90. Lissajous Hoodie – INTEGER RATIOS CLOSE | Pixelated PhysicsHoodie \[x = A\sin(3\omega t),\qquad y = B\sin(2\omega t + \pi/2)\]\[\text{closed iff }\omega_x/\omega_y\in\mathbb{Q}\]
  91. Ludwig Boltzmann Sticker – There Are More Ways To Be A Mess. | Physics StickerPaper products \[S = k_B \ln W\]\[\begin{gathered} k_B = 1.380\,649\times10^{-23}\ \text{J/K} \\ (\text{exact since 2019}) \end{gathered}\]
  92. Mach Cone Hoodie – IT ARRIVES BEFORE ITS NOISE | Pixelated PhysicsHoodie \[\sin\mu = \frac{c}{v} = \frac{1}{M}\]\[M = 2 \;\Rightarrow\; \mu = 30^\circ\]\[r_n = c\,(t - t_n),\qquad x_n = v\,t_n\]
  93. Magnara – Magnus Effect Physics StickerPaper products \[\mathbf{F}_M = \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]\[m\dot{\mathbf{v}} = m\mathbf{g} - b\mathbf{v} + \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]
  94. Magnetic Dipole Hoodie – EVERY LINE COMES HOME | Pixelated PhysicsHoodie \[\nabla\cdot\mathbf{B} = 0\]\[\mathbf{B} = \frac{\mu_0}{4\pi}\,\frac{3(\mathbf{m}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}} - \mathbf{m}}{r^3}\]\[r = C\sin^2\theta\;\text{(field lines)}\]
  95. Magnetron Twins – Electromagnetism / Polarity Lock Physics T-ShirtT-Shirt \[U = -\frac{\mu_0}{4\pi r^{3}}\left[3(\vec m_1\cdot\hat r)(\vec m_2\cdot\hat r) - \vec m_1\cdot\vec m_2\right]\]
  96. Maria Goeppert Mayer Sticker – A Full Floor Is Magic. | Physics StickerPaper products \[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ \begin{aligned} g_N &= (N+1)(N+2) \\ &= 2,\,6,\,12,\,\ldots \end{aligned} \\ \Rightarrow\; \text{shells close at } 2,\,8,\,20 \end{gathered}\]\[\begin{gathered} V_{\ell s} = -C(r)\,\vec\ell\cdot\vec s \\ j = \ell\pm\tfrac12,\ \text{degeneracy } 2j+1 \\ \Rightarrow\ 28,\,50,\,82,\,126 \end{gathered}\]
  97. Marie Curie Sticker – She Literally Glowed Up | Physics StickerPaper products \[N(t) = N_0 e^{-\lambda t}\]\[t_{1/2} = \frac{\ln 2}{\lambda}, \qquad A = \lambda N\]
  98. Max Planck Sticker – He Quantized the Vibe | Physics StickerPaper products \[E = h\nu\]\[B_\nu(\nu,T) = \frac{2h\nu^{3}}{c^{2}}\,\frac{1}{e^{h\nu/(k_B T)} - 1}\]
  99. Maxwellion – Maxwell’s Equations Physics MugMug \[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}\]\[\nabla\cdot\vec B = 0\]\[\nabla\times\vec E = -\frac{\partial\vec B}{\partial t}\]\[\begin{gathered} \nabla\times\vec B = \mu_0\vec J \\ {}+ \mu_0\varepsilon_0\frac{\partial\vec E}{\partial t} \end{gathered}\]\[c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\]
  100. Michael Faraday Sticker – All Quiet In Here. | Physics StickerPaper products \[\oint_S \vec E\cdot d\vec A = \frac{Q_{\text{enc}}}{\varepsilon_0}\]\[\begin{gathered} \vec E_{\text{inside}} = 0 \\ (\text{empty cavity in a closed} \\ \text{conductor, electrostatic} \\ \text{equilibrium}) \end{gathered}\]
  101. Moderon – Neutron Moderation / Elastic Scattering Physics StickerPaper products \[\alpha = \left(\frac{A-1}{A+1}\right)^2\]\[\xi = 1 + \frac{\alpha\ln\alpha}{1-\alpha}\]\[n_{\text{coll}} \approx \frac{\ln(E_0/E_{\text{th}})}{\xi}\]
  102. Muonaut – Muon Time Dilation / Length Contraction Physics StickerPaper products \[\Delta t = \gamma\,\tau, \qquad L = \frac{L_0}{\gamma}\]\[\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}\]\[c\tau \approx 659\ \text{m}\]
  103. Neutrina Fade – Neutrino Ghost Matter Physics T-ShirtT-Shirt \[\cos\theta_C = \frac{1}{n\beta}\]\[P_{\nu_a\to\nu_b} = \sin^{2}(2\theta)\,\sin^{2}\!\left(\frac{\Delta m^{2}c^{4}L}{4\hbar c E}\right)\]
  104. Neutrina Fade – Neutrino Oscillation Physics MugMug \[P \approx \sin^{2}(2\theta)\,\sin^{2}\!\left(\frac{1.27\,\Delta m^{2}[\text{eV}^2]\,L[\text{km}]}{E[\text{GeV}]}\right)\]\[P(\nu_a\to\nu_b) = \sin^{2}(2\theta)\,\sin^{2}\!\left(\frac{\Delta m^{2}c^{4}L}{4\hbar c E}\right)\]
  105. Niels Bohr Sticker – Said Nothing Clearly. Explained Everything. | Physics StickerPaper products \[\begin{gathered} E_n = -\frac{R_\infty hc}{n^{2}} \\ R_\infty hc = 13.605\,693\,122\,990\ \text{eV} \end{gathered}\]\[h\nu = E_i - E_f\]
  106. Nikola Tesla Sticker – AC Slays DC Pixel Art | Physics StickerPaper products \[V(t) = V_0\sin(\omega t)\]\[\frac{V_s}{V_p} = \frac{N_s}{N_p}\]\[P_{\text{loss}} = I^{2}R\]
  107. Nodal Lines Hoodie – STILLNESS IS A PATTERN | Pixelated PhysicsHoodie \[D\,\nabla^4 w = \rho h\,\omega^2 w,\qquad D = \frac{E h^3}{12(1-\nu^2)}\]\[w(x,y) \approx \cos 7\pi x\,\cos 3\pi y - \cos 3\pi x\,\cos 7\pi y\]\[\text{sand stays where } w = 0\]
  108. Null Beacon – Cosmic Event Horizon / Causal Disconnect Physics T-ShirtT-Shirt \[d_{\text{EH}}(t) = a(t)\int_{t}^{\infty} \frac{c\,dt^{\prime}}{a(t^{\prime})}\]\[d_{\text{EH}} \to \frac{c}{H_\Lambda} \quad (\text{pure de Sitter})\]
  109. Null Beacon – Cosmic Event Horizon Physics MugMug \[d_{EH} \to \frac{c}{H_\Lambda}\quad\text{(pure de Sitter limit)}\]\[d_{EH}(t) = a(t)\int_{t}^{\infty}\frac{c\,dt'}{a(t')}\]\[H_\Lambda = H_0\sqrt{\Omega_\Lambda}\]
  110. Ohmbert – Ohm’s Law Physics MugMug \[V = I\,R\]\[P = I^{2}R\]
  111. Ole Rømer Sticker – Io Isn’t Late. Light Is. | Physics StickerPaper products \[\Delta t = \frac{\Delta d}{c}\]\[\begin{gathered} \frac{2\,\text{AU}}{c} \approx 998\ \text{s} \approx 16.6\ \text{min} \\ (\text{R\o mer's estimate} \approx 22\ \text{min}) \end{gathered}\]\[c = 299\,792\,458\ \text{m/s (exact)}\]
  112. On Cosmic Time Sticker Sheet – Muonaut, Orbitick, Relicta & Primordix | 9 Pixel Art StickersPaper products \[\begin{gathered} \Delta t = \gamma\,\tau, \qquad L = \frac{L_0}{\gamma} \\ \gamma = \frac{1}{\sqrt{1 - v^2/c^2}} \end{gathered}\]\[\begin{gathered} \frac{\Delta f}{f} \approx \frac{\Delta\Phi}{c^2} - \frac{v^2}{2c^2} \end{gathered}\]\[\begin{gathered} T(z) = T_0\,(1+z) \\ T_0 = 2.72548\ \text{K} \end{gathered}\]\[\begin{gathered} Y_p \simeq \frac{2\,(n/p)}{1 + n/p} \\ \begin{gathered} \frac{n}{p} \approx \frac{1}{7} \;\Rightarrow \\ Y_p \approx \frac{2/7}{8/7} = 0.25 \end{gathered} \end{gathered}\]
  113. Orbitick – GPS Clock Correction / Gravitational Time Dilation Physics StickerPaper products \[\frac{\Delta f}{f} \approx \frac{\Delta\Phi}{c^2} - \frac{v^2}{2c^2}\]\[\frac{\Delta f}{f} = +4.4647\times10^{-10}\]\[\begin{aligned} f_0 &= 10.23\ \text{MHz} \\ &\quad\times(1 - 4.4647\times10^{-10}) \\ &= 10.229\,999\,995\,43\ \text{MHz} \end{aligned}\]
  114. Oscillayne – The Harmonic Pulse / Waveform Resonance Physics T-ShirtT-Shirt \[\ddot x + \gamma\dot x + \omega_0^{2}x = \frac{F_0}{m}\cos\omega t\]\[A(\omega) = \frac{F_0/m}{\sqrt{(\omega_0^{2}-\omega^{2})^{2} + \gamma^{2}\omega^{2}}}\]