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カタログのすべての方程式を、商品ごとに一行で。

1. Arnold's Cat – Cat Map Chaos Physics T-ShirtT-Shirt \[\Gamma:\ (x, y) \mapsto (x + y,\ x + 2y) \bmod 1\]\[A = \begin{pmatrix}1 & 1\\ 1 & 2\end{pmatrix},\quad \det A = 1,\quad \lambda_\pm = \frac{3 \pm \sqrt{5}}{2}\]\[\Pi(124) = 15\]
2. Azurwake – Cherenkov Radiation / Light-Speed in Water Physics StickerPaper products \[\cos\theta = \frac{1}{n\beta}, \qquad \beta > \frac{1}{n}\]\[\begin{aligned} \frac{d^2N}{dx\,d\lambda} &= \frac{2\pi\alpha z^2}{\lambda^2} \\ &\quad\times\left(1-\frac{1}{\beta^2 n^2}\right) \end{aligned}\]
3. Bifurcor – Stern–Gerlach Experiment / Spin Quantization Physics StickerPaper products \[F_z = \mu_z\,\frac{\partial B_z}{\partial z}\]\[\begin{gathered} \mu_z = -g_s\,\mu_B\,m_s \\ m_s = \pm\tfrac{1}{2} \end{gathered}\]
4. Bose-Einstein Condensate 1995 TeeT-Shirt \[\lambda_{\mathrm{dB}} = \frac{h}{\sqrt{2\pi m k_B T}}\]\[n\,\lambda_{\mathrm{dB}}^{3} = \zeta(3/2) \approx 2.612\]\[k_B T_c = \frac{2\pi\hbar^{2}}{m}\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\quad\text{(uniform gas)}\]\[k_B T_c \approx 0.94\,\hbar\bar\omega\,N^{1/3}\quad\text{(harmonic trap)}\]
5. Bremsella – Bremsstrahlung (Braking Radiation) Physics StickerPaper products \[P = \frac{q^2 a^2}{6\pi\varepsilon_0 c^3}\]
6. C. V. Raman Sticker – Most Pass Free. A Few Pay A Toll. | Physics StickerPaper products \[\begin{gathered} h\nu_s = h\nu_0 - h\nu_{\text{vib}} \\ (\text{Stokes}) \end{gathered}\]\[\begin{gathered} h\nu_s = h\nu_0 + h\nu_{\text{vib}} \\ (\text{anti-Stokes}) \end{gathered}\]\[\Delta\tilde\nu = \frac{1}{\lambda_0} - \frac{1}{\lambda_s}\]
7. Casimira – The Casimir Effect Pixel StickerPaper products \[\frac{F}{A} = -\frac{\pi^2\hbar c}{240\,d^4}\]
8. Cecilia Payne-Gaposchkin Sticker – Almost Certainly Real. | Physics StickerPaper products \[\begin{aligned} \frac{n_{i+1}\,n_e}{n_i} &= \frac{2}{\Lambda^{3}}\,\frac{g_{i+1}}{g_i} \\ &\quad\times\exp\!\left(-\frac{\chi_i}{k_B T}\right) \\ \Lambda &= \frac{h}{\sqrt{2\pi m_e k_B T}} \end{aligned}\]\[\begin{gathered} X + Y + Z = 1 \\ (\text{Sun's surface today:} \\ X\approx0.74,\ Y\approx0.25, \\ Z\approx0.013) \end{gathered}\]
9. Chandrasekhar Limit Tee: 1.4 M☉T-Shirt \[M_{\mathrm{Ch}} = \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2}\frac{1}{(\mu_e m_H)^{2}} \approx \frac{5.8\,M_\odot}{\mu_e^{2}}\]\[\mu_e = 2 \;\Rightarrow\; M_{\mathrm{Ch}} \approx 1.44\,M_\odot\ \text{(ideal)},\ \approx 1.4\,M_\odot\ \text{(real white dwarfs)}\]
10. Chien-Shiung Wu Sticker – She Broke Symmetry. And Records. | Physics StickerPaper products \[{}^{60}\mathrm{Co} \to {}^{60}\mathrm{Ni}^{*} + e^{-} + \bar\nu_e\]\[\begin{gathered} \hat P:\ \vec J \to \vec J,\ \ \vec p_e \to -\vec p_e \\ \Rightarrow\; \langle \vec J\cdot\vec p_e\rangle \ne 0 \\ \text{violates parity} \end{gathered}\]
11. Christiaan Huygens Sticker – Every Point A Source | Physics StickerPaper products \[r = v\,\Delta t\]\[\text{new front} = \text{envelope of the wavelets}\]
12. Condensa – Bose–Einstein Condensate Physics StickerPaper products \[\frac{N_0}{N} = 1 - \left(\frac{T}{T_c}\right)^{3/2}\quad(T\le T_c)\]\[kT_c = \frac{2\pi\hbar^2}{m}\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\]
13. Corekeeper – Strong Nuclear Force / Nuclear Binding Physics T-ShirtT-Shirt \[V(r) = -\frac{g^{2}}{4\pi}\frac{e^{-r/\lambda}}{r}, \qquad \lambda = \frac{\hbar}{m_\pi c}\]\[B = \left(Z m_p + N m_n - M_{\text{nuc}}\right)c^{2}\]
14. Coriolix – Coriolis Effect Physics StickerPaper products \[\mathbf{a}' = -2\,\boldsymbol{\Omega}\times\mathbf{v}' - \boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\mathbf{r}')\]\[x' = vt\cos\Omega t,\qquad y' = -vt\sin\Omega t\]\[\Delta\varphi = \frac{\Omega R}{v}\]
15. Cryo Fault – Ductile-to-Brittle Transition Physics T-ShirtT-Shirt \[\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}\]\[K_I = Y\sigma\sqrt{\pi a} \ \ge\ K_{Ic} \;\Rightarrow\; \text{fracture}\]
16. Dark Matter Host – Gravitational Lensing / Invisible Mass Physics T-ShirtT-Shirt \[v(r)^{2} = \frac{G M(r)}{r} \;\Rightarrow\; M(r) = \frac{v^{2} r}{G}\]\[\theta_E = \sqrt{\frac{4GM}{c^{2}}\,\frac{D_{LS}}{D_L D_S}}\]
17. Decay Dancer – Weak Nuclear Force / Beta Decay Physics T-ShirtT-Shirt \[n \to p + e^{-} + \bar\nu_e\]\[d \to u + W^{-} \to u + e^{-} + \bar\nu_e\]\[Q = \left(m_n - m_p - m_e\right)c^{2} \approx 0.782\ \text{MeV}\]
18. Decoherex – The Interference / Quantum Decoherence Physics T-ShirtT-Shirt \[\rho_{01}(t) = \rho_{01}(0)\,e^{-t/\tau_D}\]
19. Diagonix – Malus’s Law / Three-Polarizer Effect Physics StickerPaper products \[I = I_0\cos^2\theta\]\[I_{\text{out}} = \frac{I_0}{2}\cos^2 45^\circ\,\cos^2 45^\circ\]\[I_{\text{out}} = \frac{I_0}{8}\]
20. Émilie du Châtelet Sticker – 2× The Speed. 4× The Dent. | Physics StickerPaper products \[\begin{gathered} E_k = \tfrac{1}{2} m v^{2} \\ (\text{vis viva: } m v^{2}) \end{gathered}\]\[v = \sqrt{2 g h}\;\Rightarrow\; h \propto v^{2}\]\[\begin{gathered} m g h \approx F d\;\Rightarrow\; d \propto v^{2} \\ (\text{idealised: constant} \\ \text{clay resistance}) \end{gathered}\]\[\begin{gathered} m_1 h_1 = m_2 h_2 \\ \Leftrightarrow\; m_1 v_1^{2} = m_2 v_2^{2} \\ \Rightarrow\; \text{equal dents} \\ (\text{'s Gravesande}) \end{gathered}\]
21. Emmy Noether Sticker – Symmetry In. Conservation Out. | Physics StickerPaper products \[Q = \sum_i \frac{\partial L}{\partial \dot q_i}\,\delta q_i\]\[\delta L = 0 \;\Rightarrow\; \frac{dQ}{dt} = 0\]\[\begin{gathered} E = \sum_i \dot q_i\,\frac{\partial L}{\partial \dot q_i} - L \\ \frac{\partial L}{\partial t} = 0 \;\Rightarrow\; \frac{dE}{dt} = 0 \end{gathered}\]\[\begin{aligned} t \to t+\epsilon \;&\Rightarrow\; E \text{ conserved} \\ \vec x \to \vec x+\vec\epsilon \;&\Rightarrow\; \vec p \\ \theta \to \theta+\epsilon \;&\Rightarrow\; \vec L \end{aligned}\]
22. Enrico Fermi Sticker – Within An Order | Physics StickerPaper products \[f(E)=\frac{1}{e^{(E-\mu)/kT}+1}\]\[f(\mu)=\tfrac12\quad(T>0)\]
23. Ernest Rutherford Sticker – Some Came Back | Physics StickerPaper products \[\frac{d\sigma}{d\Omega} = \left(\frac{zZe^2}{16\pi\varepsilon_0 E}\right)^2\frac{1}{\sin^4(\theta/2)}\]\[\tan\frac{\theta}{2} = \frac{d}{2b},\qquad d = \frac{zZe^2}{4\pi\varepsilon_0 E}\]
24. Eventide Prophet – Black Hole Information Paradox Physics T-ShirtT-Shirt \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[S_{BH} = \frac{k_B c^{3} A}{4 G \hbar}\]\[\begin{gathered} S_{\text{rad}}(t) \le S_{BH}(t) \\ \text{unitary evaporation} \\ (\text{Page 1993}) \end{gathered}\]
25. Exclusor – Pauli Exclusion Principle / Degeneracy Pressure Physics T-ShirtT-Shirt \[\psi(x_1,x_2) = \frac{1}{\sqrt{2}}\begin{vmatrix} \phi_a(x_1) & \phi_b(x_1) \\ \phi_a(x_2) & \phi_b(x_2) \end{vmatrix}\]\[\psi(x_2,x_1) = -\,\psi(x_1,x_2)\]\[\phi_a = \phi_b \;\Rightarrow\; \psi = 0\]\[P = \frac{(3\pi^{2})^{2/3}}{5}\,\frac{\hbar^{2}}{m_e}\,n_e^{5/3}\]
26. Expulsieur – Meissner Effect / Flux Expulsion Physics StickerPaper products \[\mathbf{B}_{\text{inside}} = 0\]\[B(x) = B_0\,e^{-x/\lambda_L}\]\[\lambda_L = \sqrt{\frac{m}{\mu_0 n_s e^2}}\]
27. Fritz Zwicky Sticker – Too Fast To Be Lit | Physics StickerPaper products \[\sigma^2 \sim \frac{GM}{R}\]\[M_{\mathrm{vir}} \approx \frac{\sigma^2 R}{G}\]
28. Galileo Galilei Sticker – Telescope. Tea. Trouble with the Church. | Physics StickerPaper products \[d = \tfrac{1}{2}g t^{2}\]\[d_1 : d_2 : d_3 : \dots = 1 : 3 : 5 : \dots\]
29. Graviton Whisper – Quantum Gravity / Force Carrier Physics T-ShirtT-Shirt \[\Box\,\bar h_{\mu\nu} = -\frac{16\pi G}{c^{4}}\,T_{\mu\nu}\]\[E = hf, \qquad m_{g} = 0 \ (\text{if it exists}),\ \ s = 2\]\[m_g \le 2.42\times10^{-23}\ \mathrm{eV}/c^{2}\quad\text{(LIGO–Virgo–KAGRA, GWTC-3, 90\% credible)}\]
30. Gyrolla – Cyclotron Motion / Lorentz Force Physics StickerPaper products \[q v B = \frac{m v^2}{r} \;\Rightarrow\; r = \frac{m v}{q B}\]\[f_c = \frac{q B}{2\pi m}\]\[\frac{f_c}{B} \approx 15.2\ \text{MHz/T}\ (\text{proton})\]
31. Hadron Brawler – Strong Nuclear Force / Quantum Chromodynamics Physics T-ShirtT-Shirt \[V(r) = -\frac{4}{3}\frac{\alpha_s \hbar c}{r} + \sigma r\]
32. Henrietta Swan Leavitt Sticker – The Blink Is the Ruler | Physics StickerPaper products \[M_V = -2.43\,(\log_{10} P - 1) - 4.05\]\[m - M = 5\log_{10}\frac{d}{10\,\mathrm{pc}}\]
33. Hideki Yukawa Sticker – Heavy Ball. Short Game. | Physics StickerPaper products \[\begin{gathered} V(r) = -\frac{g^{2}}{4\pi}\,\frac{e^{-r/R}}{r} \\ R = \frac{\hbar}{m c} \end{gathered}\]\[\begin{aligned} R &= \frac{1}{\lambda} = 2\ \text{fm} \\ \Rightarrow\; mc^{2} &= \frac{\hbar c}{R} \approx 99\ \text{MeV} \\ &\approx 2\times10^{2}\,m_e c^{2} \end{aligned}\]
34. Interfera – The Path Unchosen / Quantum Interference Physics T-ShirtT-Shirt \[P = \lvert\psi_1 + \psi_2\rvert^{2} = \lvert\psi_1\rvert^{2} + \lvert\psi_2\rvert^{2} + 2\,\mathrm{Re}\!\left(\psi_1^{*}\psi_2\right)\]\[\Delta y = \frac{\lambda L}{d}, \qquad \lambda = \frac{h}{p}\]
35. Invertia – Negative Absolute Temperature / Population Inversion Physics StickerPaper products \[\frac{1}{T} = \frac{\partial S}{\partial E} < 0\]\[\frac{N_{\uparrow}}{N_{\downarrow}} = e^{-\Delta E/k_B T}\]\[T < 0 \;\Rightarrow\; N_{\uparrow} > N_{\downarrow}\]
36. Isaac Newton Sticker – Gravity Hits Different | Physics StickerPaper products \[\vec F = \frac{d\vec p}{dt}\]\[F = \frac{G m_1 m_2}{r^{2}}\]
37. James Clerk Maxwell Sticker – Field Goals Achieved | Physics StickerPaper products \[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}, \quad \nabla\cdot\vec B = 0\]\[\nabla\times\vec E = -\frac{\partial\vec B}{\partial t}, \quad \nabla\times\vec B = \mu_0\vec J + \mu_0\varepsilon_0\frac{\partial\vec E}{\partial t}\]\[c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\]
38. Jocelyn Bell Burnell Sticker – She Found Pulsars. They Gave Her Silence. | Physics StickerPaper products \[\bar\rho \gtrsim \frac{3\pi}{G P^{2}}\]\[\Delta t = \frac{e^{2}}{8\pi^{2}\varepsilon_0 m_e c}\,\mathrm{DM}\left(f_1^{-2} - f_2^{-2}\right)\]
39. Lenzor – Lenz’s Law / Eddy-Current Braking Physics StickerPaper products \[\mathcal{E} = -\frac{d\Phi_B}{dt}\]\[m g = F_{\text{eddy}}(v_t) \propto \sigma\,v_t\]
40. Libratrix – Lagrange Points / Three-Body Equilibrium Physics StickerPaper products \[r_{L2} \approx R\left(\frac{M_2}{3M_1}\right)^{1/3}\]\[r_{L2} \approx 1.5\times10^{6}\ \text{km}\]\[\frac{M_1}{M_2} > \frac{25+\sqrt{621}}{2} \approx 24.96\]
41. Lise Meitner Sticker – Split Happens | Physics StickerPaper products \[Q = \left(M_{\text{initial}} - M_{\text{final}}\right)c^{2}\]\[E_C = \frac{Z_1 Z_2 e^{2}}{4\pi\varepsilon_0\,d}\]
42. Ludwig Boltzmann Sticker – There Are More Ways To Be A Mess. | Physics StickerPaper products \[S = k_B \ln W\]\[\begin{gathered} k_B = 1.380\,649\times10^{-23}\ \text{J/K} \\ (\text{exact since 2019}) \end{gathered}\]
43. Magnara – Magnus Effect Physics StickerPaper products \[\mathbf{F}_M = \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]\[m\dot{\mathbf{v}} = m\mathbf{g} - b\mathbf{v} + \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]
44. Magnetron Twins – Electromagnetism / Polarity Lock Physics T-ShirtT-Shirt \[U = -\frac{\mu_0}{4\pi r^{3}}\left[3(\vec m_1\cdot\hat r)(\vec m_2\cdot\hat r) - \vec m_1\cdot\vec m_2\right]\]
45. Maria Goeppert Mayer Sticker – A Full Floor Is Magic. | Physics StickerPaper products \[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ \begin{aligned} g_N &= (N+1)(N+2) \\ &= 2,\,6,\,12,\,\ldots \end{aligned} \\ \Rightarrow\; \text{shells close at } 2,\,8,\,20 \end{gathered}\]\[\begin{gathered} V_{\ell s} = -C(r)\,\vec\ell\cdot\vec s \\ j = \ell\pm\tfrac12,\ \text{degeneracy } 2j+1 \\ \Rightarrow\ 28,\,50,\,82,\,126 \end{gathered}\]
46. Marie Curie Sticker – She Literally Glowed Up | Physics StickerPaper products \[N(t) = N_0 e^{-\lambda t}\]\[t_{1/2} = \frac{\ln 2}{\lambda}, \qquad A = \lambda N\]
47. Max Planck Sticker – He Quantized the Vibe | Physics StickerPaper products \[E = h\nu\]\[B_\nu(\nu,T) = \frac{2h\nu^{3}}{c^{2}}\,\frac{1}{e^{h\nu/(k_B T)} - 1}\]
48. Michael Faraday Sticker – All Quiet In Here. | Physics StickerPaper products \[\oint_S \vec E\cdot d\vec A = \frac{Q_{\text{enc}}}{\varepsilon_0}\]\[\begin{gathered} \vec E_{\text{inside}} = 0 \\ (\text{empty cavity in a closed} \\ \text{conductor, electrostatic} \\ \text{equilibrium}) \end{gathered}\]
49. Moderon – Neutron Moderation / Elastic Scattering Physics StickerPaper products \[\alpha = \left(\frac{A-1}{A+1}\right)^2\]\[\xi = 1 + \frac{\alpha\ln\alpha}{1-\alpha}\]\[n_{\text{coll}} \approx \frac{\ln(E_0/E_{\text{th}})}{\xi}\]
50. Muonaut – Muon Time Dilation / Length Contraction Physics StickerPaper products \[\Delta t = \gamma\,\tau, \qquad L = \frac{L_0}{\gamma}\]\[\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}\]\[c\tau \approx 659\ \text{m}\]
51. Neutrina Fade – Neutrino Ghost Matter Physics T-ShirtT-Shirt \[\cos\theta_C = \frac{1}{n\beta}\]\[P_{\nu_a\to\nu_b} = \sin^{2}(2\theta)\,\sin^{2}\!\left(\frac{\Delta m^{2}c^{4}L}{4\hbar c E}\right)\]
52. Niels Bohr Sticker – Said Nothing Clearly. Explained Everything. | Physics StickerPaper products \[\begin{gathered} E_n = -\frac{R_\infty hc}{n^{2}} \\ R_\infty hc = 13.605\,693\,122\,990\ \text{eV} \end{gathered}\]\[h\nu = E_i - E_f\]
53. Nikola Tesla Sticker – AC Slays DC Pixel Art | Physics StickerPaper products \[V(t) = V_0\sin(\omega t)\]\[\frac{V_s}{V_p} = \frac{N_s}{N_p}\]\[P_{\text{loss}} = I^{2}R\]
54. Null Beacon – Cosmic Event Horizon / Causal Disconnect Physics T-ShirtT-Shirt \[d_{\text{EH}}(t) = a(t)\int_{t}^{\infty} \frac{c\,dt^{\prime}}{a(t^{\prime})}\]\[d_{\text{EH}} \to \frac{c}{H_\Lambda} \quad (\text{pure de Sitter})\]