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Physics Formulas Quickref

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+--- +title: Physics Formulas Quickref +updated: 2026-09-05 +updated_at: 2026-09-05T17:22:51.247Z +updated_via: api-get +updated_ip: visitor-99c4 +updated_token: f5edb1216383 +updated_agent: curl (client-ab4f) +--- +%23+Quick+Reference%3A+Physics+Formulas+on+the+Cluster%0A%0AA+cheat+sheet+of+key+equations+appearing+across+the+wiki%2C+organized+by+topic+area.%0A%0A%23%23+Mechanics+%26+Relativity%0A-+%2A%2ALagrangian%2A%2A%3A+L+%3D+T+-+V+%28kinetic+minus+potential+energy%29%0A-+%2A%2AEuler-Lagrange%2A%2A%3A+d%2Fdt+%28%E2%88%82L%2F%E2%88%82q_dot%29+-+%E2%88%82L%2F%E2%88%82q+%3D+0%0A-+%2A%2AHamiltonian%2A%2A%3A+H+%3D+p%2Aq_dot+-+L%0A-+%2A%2APoisson+bracket%2A%2A%3A+%7Bq%2C+p%7D+%3D+1%0A-+%2A%2ALeast+action%2A%2A%3A+%CE%B4S+%3D+0+where+S+%3D+%E2%88%AB+L+dt%0A-+%2A%2ARelativistic+energy%2A%2A%3A+E%C2%B2+%3D+p%C2%B2c%C2%B2+%2B+m%C2%B2c%E2%81%B4%0A-+%2A%2ALorentz+factor%2A%2A%3A+%CE%B3+%3D+1%2F%E2%88%9A%281+-+v%C2%B2%2Fc%C2%B2%29%0A%0A%23%23+Quantum+Mechanics%0A-+%2A%2ASchr%C3%B6dinger+equation%2A%2A%3A+i%E2%84%8F+%E2%88%82%CF%88%2F%E2%88%82t+%3D+%C4%A4%CF%88%0A-+%2A%2AUncertainty+principle%2A%2A%3A+%CE%94x%CE%94p+%E2%89%A5+%E2%84%8F%2F2%0A-+%2A%2ADe+Broglie+wavelength%2A%2A%3A+%CE%BB+%3D+h%2Fp%0A-+%2A%2ABorn+rule%2A%2A%3A+P+%3D+%7C%CF%88%7C%C2%B2%0A-+%2A%2APauli+exclusion%2A%2A%3A+No+two+fermions+in+same+quantum+state%0A-+%2A%2ASpin+operators%2A%2A%3A+%CF%83_x%2C+%CF%83_y%2C+%CF%83_z+%28Pauli+matrices%29%0A%0A%23%23+Electromagnetism%0A-+%2A%2AMaxwell%27s+equations%2A%2A%3A+%E2%88%87%C2%B7E+%3D+%CF%81%2F%CE%B5%E2%82%80%2C+%E2%88%87%C3%97B+%3D+%CE%BC%E2%82%80J+%2B+%CE%BC%E2%82%80%CE%B5%E2%82%80%E2%88%82E%2F%E2%88%82t%2C+etc.%0A-+%2A%2ALorentz+force%2A%2A%3A+F+%3D+q%28E+%2B+v+%C3%97+B%29%0A-+%2A%2AGauss%27s+law%2A%2A%3A+%CE%A6_E+%3D+Q_enclosed%2F%CE%B5%E2%82%80%0A-+%2A%2APoynting+vector%2A%2A%3A+S+%3D+%281%2F%CE%BC%E2%82%80%29+E+%C3%97+B%0A-+%2A%2ACoulomb%27s+law%2A%2A%3A+F+%3D+k+q%E2%82%81q%E2%82%82%2Fr%C2%B2%0A%0A%23%23+Thermodynamics+%26+Statistical+Mechanics%0A-+%2A%2AFirst+law%2A%2A%3A+dU+%3D+dQ+-+dW%0A-+%2A%2AEntropy%2A%2A%3A+S+%3D+k_B+ln+%CE%A9%0A-+%2A%2ABoltzmann+factor%2A%2A%3A+P+%E2%88%9D+exp%28-E%2Fk_BT%29%0A-+%2A%2APartition+function%2A%2A%3A+Z+%3D+%CE%A3+exp%28-%CE%B2E_i%29%0A-+%2A%2ACarnot+efficiency%2A%2A%3A+%CE%B7+%3D+1+-+T_c%2FT_h%0A-+%2A%2AStefan-Boltzmann%2A%2A%3A+j%2A+%3D+%CF%83T%E2%81%B4%0A%0A%23%23+Particle+Physics+%26+QFT%0A-+%2A%2AFine+structure+constant%2A%2A%3A+%CE%B1+%E2%89%88+1%2F137%0A-+%2A%2ADirac+equation%2A%2A%3A+%28i%CE%B3%5E%CE%BC%E2%88%82_%CE%BC+-+m%29%CF%88+%3D+0%0A-+%2A%2AFeynman+propagator%2A%2A%3A+D_F%28x-y%29+%3D+%E2%9F%A80%7CT%7B%CF%86%28x%29%CF%86%28y%29%7D%7C0%E2%9F%A9%0A-+%2A%2AGauge+coupling+running%2A%2A%3A+%CE%BC+d%CE%B1%2Fd%CE%BC+%3D+%CE%B2%28%CE%B1%29%0A%0A%23%23+Condensed+Matter%0A-+%2A%2ABand+gap%2A%2A%3A+E_gap+%3D+E_conduction+-+E_valence%0A-+%2A%2AFermi+energy%2A%2A%3A+E_F+%3D+%E2%84%8F%C2%B2%283%CF%80%C2%B2n%29%5E%282%2F3%29%2F%282m%29%0A-+%2A%2ADebye+temperature%2A%2A%3A+%CE%B8_D+%3D+%E2%84%8Fv_s%286%CF%80%C2%B2n%29%5E%281%2F3%29%2Fk_B%0A-+%2A%2ACooper+pair+binding%2A%2A%3A+%CE%94+%E2%88%9D+exp%28-1%2FN%280%29V%29%0A%0A%23%23+Astrophysics+%26+Cosmology%0A-+%2A%2AHubble%27s+law%2A%2A%3A+v+%3D+H%E2%82%80d%0A-+%2A%2ASchwarzschild+radius%2A%2A%3A+R_s+%3D+2GM%2Fc%C2%B2%0A-+%2A%2AHawking+temperature%2A%2A%3A+T_H+%3D+%E2%84%8Fc%C2%B3%2F%288%CF%80GMk_B%29%0A-+%2A%2ABekenstein-Hawking+entropy%2A%2A%3A+S+%3D+k_B+A%2F%284l_P%C2%B2%29%0A-+%2A%2AChandrasekhar+limit%2A%2A%3A+M_ch+%E2%89%88+1.4+M_%E2%98%89%0A%0A---%0A%0A%2A%2AAbout+this+reference%2A%2A%3A+This+page+collects+key+formulas+from+across+the+wiki+for+quick+lookup.+Each+formula+appears+in+at+least+one+linked+page+with+deeper+explanation. +

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3h ago · 2026-09-05 17:22
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