Newton's Three Laws of Motion


Lagrangian Mechanics (Principle of Least Action)


Hamiltonian Mechanics


Hamilton-Jacobi Equation


Euler-Lagrange Equation


D'Alembert's Principle


Euler's Rigid Body Rotation Equations


Conservation of Momentum


Conservation of Angular Momentum


Conservation of Energy


Work-Energy Theorem


Impulse-Momentum Theorem


Center of Mass Equation


Hooke's Law


Parallel Axis Theorem


Coriolis Force


Centrifugal Force


Simple Harmonic Motion


Damped Harmonic Oscillator


Forced Oscillator + Resonance


Coupled Oscillators (Normal Modes)


Pendulum Equation


Kinematics (Constant Acceleration)


Universal Gravitation Law


Gravitational Potential Energy


Kepler's First Law


Kepler's Second Law


Kepler's Third Law


Escape Velocity


Orbital Velocity (Circular)


Poisson Equation (Gravity)


Tidal Force


Gravitational Time Dilation (GR)


Precession of Perihelion (GR)


Lense-Thirring Precession (Frame Dragging)


Coulomb's Law


Lorentz Force Law


Maxwell's Equations (Differential)


Maxwell's Equations (Integral)


Scalar and Vector Potentials


Gauge Invariance (U(1) in E&M)


Biot-Savart Law


Ampère's Force Law (Wire)


Ohm's Law


Kirchhoff's Current Law (KCL)


Kirchhoff's Voltage Law (KVL)


Faraday's Law of Induction


Lenz's Law


Poynting's Theorem


Electromagnetic Wave Equation


EM Stress-Energy Tensor


Lienard-Wiechert Potentials


Larmor Formula (Non-rel. Radiation)


Liénard Formula (Relativistic Radiation)


Abraham-Lorentz Force (Radiation Reaction)


Coulomb Gauge


Lorenz Gauge


RC Circuit Charging


Ideal Gas Law


Equipartition Theorem


Carnot Efficiency


Clausius-Clapeyron Relation


Gibbs Phase Rule


Helmholtz Free Energy


Gibbs Free Energy


Enthalpy


Maxwell Relations (Thermodynamics)


TdS Equations


Specific Heat Relations (C_p−C_V)


Joule-Thomson Coefficient


Entropy of Mixing


Planck's Blackbody Radiation Law


Wien's Displacement Law


Stefan-Boltzmann Law


Photoelectric Effect Equation (Einstein)


Einstein A and B Coefficients


Compton Scattering Formula


de Broglie Wavelength


Schrödinger Equation (Time-Dependent)


Time-Independent Schrödinger Equation


Born Rule (Probability Interpretation)


Probability Current (QM)


Canonical Commutation Relations


Heisenberg Uncertainty Principle


Harmonic Oscillator Energy Levels (QM)


Hydrogen Atom Energy Levels


Angular Momentum Quantization


Spin-½ Algebra (Pauli Matrices)


Spin-Orbit Coupling


Dirac Equation


Klein-Gordon Equation


Fine Structure Formula (Hydrogen)


Lamb Shift


Anomalous Magnetic Moment (Electron)


Pauli Exclusion Principle


Spin-Statistics Theorem


Fermi's Golden Rule


Time-Dependent Perturbation Theory (1st Order)


WKB Approximation


Born Approximation (Scattering)


Partial Wave Expansion (Scattering)


Optical Theorem


Feynman Path Integral


Von Neumann Equation


Ehrenfest Theorem


Bell's Inequality


Lorentz Transformations (Boost)


Minkowski Spacetime Interval


Time Dilation


Length Contraction


Relativistic Energy-Momentum Relation


Mass-Energy Equivalence


Relativistic Doppler Effect


Relativistic Velocity Addition


Einstein Field Equations (GR)


Einstein-Hilbert Action


Schwarzschild Metric


Kerr Metric (Rotating Black Hole)


FLRW Metric


Geodesic Equation


Gravitational Wave (TT Gauge)


Bekenstein-Hawking Black Hole Entropy


Black Hole Area Theorem (Hawking 1971)


QCD Beta Function (1-loop)


DGLAP Evolution Equations


CKM Matrix (Quark Mixing)


PMNS Matrix (Neutrino Mixing)


Gell-Mann–Oakes–Renner Relation


Higgs Mechanism (Mass Generation)


Weinberg Angle


Faddeev-Popov Gauge Fixing + Ghosts


BRST Symmetry


Running Coupling (RGE, General)


Fermi's Theory (4-Fermion, Low-Energy EW)


Pati-Salam Model (SU(4)×SU(2)×SU(2))


Axion (Peccei-Quinn Solution to Strong CP)


Muon g−2 Anomaly


First Friedmann Equation


Second Friedmann Equation


Cosmological Fluid Equation


Redshift Relation


Hubble-Lemaître Law


CMB Blackbody Spectrum


BBN Primordial Element Abundances


Sound Horizon at Recombination


Sachs-Wolfe Effect (CMB)


Dark Energy Equation of State


Deceleration Parameter


Matter Power Spectrum


Cosmic Distance Ladder Relations


Hubble Tension


S₈ Tension


Age of the Universe


Navier-Stokes Equation (Incompressible)


Continuity Equation (Fluid)


Euler Equation (Inviscid)


Bernoulli's Equation


Stokes Law (Drag on Sphere)


Poiseuille Flow (Hagen-Poiseuille)


Reynolds Number


Froude Number


Kutta-Joukowski Theorem (Lift)


Torricelli's Law (Efflux Speed)


Surface Tension (Young-Laplace)


Thin Lens Equation


Grating Equation


Malus's Law


Abbe Sine Condition


Fermat's Principle of Least Time


Fabry-Pérot Etalon Transmission


Critical Angle (Total Internal Reflection)


Shock Wave Rankine-Hugoniot Relations


Beat Frequency


Kronig-Penney Model (1D Band Structure)


Fermi-Dirac Distribution


Free Electron Density of States


BCS Theory (Superconductivity)


BCS Gap Equation at T=0


London Equations (Perfect Diamagnetism)


Josephson Effects (DC + AC)


Curie's Law (Paramagnetism)


Heisenberg Exchange Interaction


Hall Effect


Debye Model (Lattice Heat Capacity)


Mott Insulator Transition


Density Functional Theory (Kohn-Sham Equations)


Landau Fermi Liquid Theory


Radioactive Decay Law


Bethe-Weizsäcker (Semi-Empirical) Mass Formula


Geiger-Nuttall Law (α-Decay)


Nuclear Shell Model (Magic Numbers)


Q-Value of Nuclear Reaction


Neutrino Oscillation Probability


Four-Factor Formula (Nuclear Reactor)


Rutherford Scattering Cross-Section


Mössbauer Effect (Recoilless γ Emission)


Breit-Wigner Resonance (Nuclear Reactions)


Lane-Emden Equation (Polytropic Stars)


Eddington Luminosity Limit


Chandrasekhar Limit (White Dwarf)


TOV Limit (Neutron Star Maximum Mass)


Hertzsprung-Russell Diagram + Main Sequence


Mass-Luminosity Relation


Virial Theorem (Astrophysics)


Jeans Instability Criterion (Star Formation)


Schwarzschild Criterion (Convection)


pp Chain Energy Release


CNO Cycle (Massive Stars)


Triple-Alpha Process (Helium Burning)


Core-Collapse Supernova Mechanism


Type Ia Supernova (Standardizable Candle)


Neutron Star Equation of State (Various)


Oppenheimer-Snyder Collapse (BH Formation)


Pulsar Spin-Down


Olbers' Paradox Resolution


Debye Length (Plasma Screening)


Plasma Frequency


Alfvén Wave Speed


MHD Induction Equation


Saha Ionization Equation


Gyro-frequency (Larmor Frequency)


Beta Parameter (Plasma Confinement)


Lawson Criterion (Fusion Ignition)


Noether's Theorem


Stokes' Theorem


Gauss's Divergence Theorem


Green's Theorem (2D)


Fourier Transform


Laplace's Equation


Poisson's Equation


Bessel's Equation


Legendre's Equation


Hermite's Equation


Associated Legendre Equation


Chebyshev Polynomials


Laguerre Polynomials


Spherical Harmonics (Y_l^m)


Gamma Function


Error Function


Delta Function (Dirac)


Eigenvalue Equation


Separation of Variables Method


Boltzmann Distribution


Canonical Partition Function


Grand Canonical Partition Function


Boltzmann Entropy Formula


Gibbs Entropy Formula


Fluctuation-Dissipation Theorem


Einstein-Smoluchowski Relation (Diffusion)


Jarzynski Equality


Crooks Fluctuation Theorem


Ising Model (1D/2D Exact Solution)


Central Limit Theorem (Statistical)


Bose-Einstein Condensation (T_c)


Kramers-Kronig Relations (Dispersion)


Cauchy Stress Principle


Infinitesimal Strain Tensor


Young's Modulus / Elastic Modulus


Shear Modulus


Bulk Modulus


Poisson's Ratio


Euler-Bernoulli Beam Equation


Timoshenko Beam Theory


Elastic Wave Speeds (P and S waves)


Creep / Viscoelastic Maxwell Model


Plastic Yield (Von Mises Criterion)


Shannon Entropy


Shannon-Hartley Channel Capacity


Nyquist-Shannon Sampling Theorem


Landauer's Principle


Kolmogorov Complexity (Algorithmic Info)


Maximum Entropy Principle (Jaynes)


Speed of Light Defines Meter


Planck Constant Defines Kilogram


Elementary Charge Defines Ampere


Boltzmann Constant Defines Kelvin


Avogadro Number Defines Mole


Josephson Voltage Standard


Quantum Hall Resistance Standard


Bragg's Law (Generalized, Powder Diffraction)


Laue Equations (3D Diffraction Condition)


Structure Factor Equation


Atomic Scattering Factor (X-ray Form Factor)


Reciprocal Lattice Vector Definition


Brillouin Zone Boundaries


Ewald Sphere Construction


Patterson Function (Interatomic Vectors)


Debye-Waller Factor (Thermal Motion)


Space Group Symmetry Operations


Interplanar Spacing (Cubic Systems)


Scherrer Equation (Crystallite Size)


Williamson-Hall Analysis (Size + Strain)


True Stress — True Strain Definition


Hollomon Equation (Work Hardening)


Hall-Petch Relationship (Grain Size Strengthening)


Orowan Equation (Precipitation Strengthening)


Schmid's Law (Critical Resolved Shear Stress)


Taylor Equation (Dislocation Strengthening)


Petch-Forwood Hardness-Yield Strength Relation


Griffith Criterion (Brittle Fracture)


Stress Intensity Factor (LEFM, Mode I)


J-Integral (Elastic-Plastic Fracture)


Paris' Law (Fatigue Crack Growth)


Basquin Equation (High-Cycle Fatigue)


Coffin-Manson Relation (Low-Cycle Fatigue)


Norton-Bailey Creep Law


Larson-Miller Parameter (Creep Rupture)


Mohr-Coulomb Failure Criterion


Drucker-Prager Yield Criterion


Weibull Distribution (Brittle Failure Statistics)


Stoney Equation (Thin Film Stress)


Debye Specific Heat Model (Full)


Dulong-Petit Law


Einstein Heat Capacity Model


Wiedemann-Franz Law (Electronic Thermal Conductivity)


Debye-Callaway Model (Lattice Thermal Conductivity)


Thermal Expansion Coefficient (Grüneisen Relation)


Grüneisen Equation of State (Solids)


Lindemann Melting Criterion


Stefan-Boltzmann Radiative Heat Transfer (Between Surfaces)


Complex Dielectric Constant


Clausius-Mossotti Relation (Polarizability)


Debye Relaxation (Dipole Response)


Cole-Cole Relaxation (Distributed)


Havriliak-Negami Relaxation


Curie-Weiss Law for Ferroelectrics (Above T_c)


Piezoelectric Constitutive Equations


Pyroelectric Coefficient


Fowler-Nordheim Tunneling (Field Emission)


Poole-Frenkel Conduction (Insulators)


Varistor I-V Characteristic (Nonlinear)


Percolation Threshold (Conductivity)


Intrinsic Carrier Concentration (Semiconductors)


Fermi Level in Doped Semiconductors


Mass Action Law (Semiconductors)


Shockley Diode Equation (Ideal)


Built-in Potential (p-n Junction)


Depletion Width (p-n Junction)


MOS Capacitor Threshold Voltage


MOSFET Drain Current (Saturation, Long Channel)


Subthreshold Swing (MOSFET)


Avalanche Breakdown (Impact Ionization)


Quantum Confinement Energy (Particle in a Box)


Brus Equation (Semiconductor Nanocrystal Band Gap)


Kane's k·p Band Model (Non-Parabolicity)


Mott Transition (Doped Semiconductor)


Anderson Localization (Disordered Materials)


Tauc Plot (Band Gap from Absorption)


Stoner Criterion (Itinerant Ferromagnetism)


Stoner-Wohlfarth Model (Single-Domain Particle)


Néel Temperature (Antiferromagnetism)


Curie Temperature (Mean-Field Ferromagnetism)


Bloch T^{3/2} Law (Magnetization at Low T)


Landau-Lifshitz-Gilbert Equation (Magnetization Dynamics)


Brown's Paradox (Domain Wall Motion)


Magnetostriction (Joule Magnetostriction)


Giant Magnetoresistance (GMR, CIP)


Tunneling Magnetoresistance (TMR, Julliere Model)


RKKY Interaction (Indirect Exchange)


Superexchange (Anderson-Goodenough-Kanamori Rules)


Complex Refractive Index (General)


Kramers-Kronig Relations (Optical Constants)


Tauc-Lorentz Model (Amorphous Semiconductor Optics)


Sellmeier Equation (Refractive Index Dispersion)


Cauchy Equation (Refractive Index Fit)


Urbach Tail (Absorption Edge)


Beer-Lambert Law (Absorption)


Kubelka-Munk Theory (Diffuse Reflectance)


Fresnel Loss at Normal Incidence


Drude Model for Free-Carrier Absorption


Forster Resonance Energy Transfer (FRET) Efficiency


Stokes Shift (Luminescence)


Dexter Energy Transfer (Exchange)


Vickers Hardness Definition


Brinell Hardness


Rockwell Hardness (Indirect)


Knoop Hardness (Thin Films / Brittle)


Nanoindentation (Oliver-Pharr Method)


Charpy Impact Toughness


Izod Impact Test


Rubber Elasticity (Gaussian Chain, Affine)


Mooney-Rivlin Equation (Hyperelastic)


Flory-Huggins Theory (Polymer Solution Free Energy)


Williams-Landel-Ferry (WLF) Equation


Arrhenius Viscosity (Above Glass Transition)


Rouse Model (Unentangled Polymer Dynamics)


Reptation Model (de Gennes, Entangled Dynamics)


Entanglement Molecular Weight


Flory-Fox Equation (T_g vs Molecular Weight)


Cahn-Hilliard Equation (Spinodal Decomposition)


Avrami Equation (Crystallization Kinetics)


Lauritzen-Hoffman Theory (Polymer Crystal Growth)


Young's Equation (Contact Angle)


Wenzel Equation (Rough Surface Wetting)


Cassie-Baxter Equation (Composite/Heterogeneous Wetting)


Laplace Pressure (Curved Interface)


Kelvin Equation (Capillary Condensation)


Langmuir Adsorption Isotherm (Monolayer)


BET Isotherm (Brunauer-Emmett-Teller, Multilayer)


Freundlich Isotherm (Heterogeneous Surfaces)


Gibbs Adsorption Equation


Amontons-Coulomb Friction Law (Dry Friction)


Archard's Law (Adhesive Wear)


Hamaker Constant (Van der Waals Between Surfaces)


DLVO Theory (Colloid Stability)


Zeta Potential (Smoluchowski Equation)


Derjaguin Approximation (Force Between Curved Surfaces)


Johnson-Kendall-Roberts (JKR) Adhesion Model


Derjaguin-Muller-Toporov (DMT) Model


Fick's First Law (Steady-State Diffusion)


Fick's Second Law (Time-Dependent Diffusion)


Diffusion Solutions (Common)


Arrhenius Diffusion Coefficient


Darken Equations (Interdiffusion / Kirkendall Effect)


Nernst-Planck Equation (Ion Transport)


Stokes-Einstein Relation (Diffusion of Spheres)


Tracer Diffusion Correlation Factor


Gibbs-Thomson Effect (Curvature Depression of Melting/Equilibrium Point)


Classical Nucleation Theory (Homogeneous)


Johnson-Mehl-Avrami-Kolmogorov (JMAK) Equation


Turnbull's Nucleation Rate (Steady-State)


Lever Rule (Phase Diagram Tie Line)


Gibbs-Thomson-Freundlich (Ostwald Ripening / LSW Theory)


Darken-Gurry Plot (Solubility Limits)


Hume-Rothery Rules (Alloy Formation)


Vegard's Law (Lattice Parameter in Solid Solutions)


Rule of Mixtures (Composite Modulus, Isostrain)


Hashin-Shtrikman Bounds (Composite Moduli)


Halpin-Tsai Equations (Short Fiber Composites)


Porosity-Young's Modulus Relation (Empirical)


Gibson-Ashby Model (Cellular Solids / Foams)


Eshelby Inclusion Problem (Stress in Ellipsoidal Inclusion)


Moss-Burstein Shift (Doped Semiconductor Absorption Edge)


Franz-Keldysh Effect (Electro-Absorption)


Pockels Effect (Linear Electro-Optic)


Kerr Effect (Quadratic Electro-Optic)


Photoconductivity (Rose Model)


Shockley-Read-Hall Recombination Rate


Auger Recombination Rate


BCS Energy Gap at T=0


Ginzburg-Landau Coherence Length


Ginzburg-Landau Penetration Depth


Ginzburg-Landau Parameter (κ)


Abrikosov Vortex Lattice (Lower/Upper Critical Fields)


Flux Pinning (Bean Critical State Model)


Little-Parks Effect (Fluxoid Quantization)


Andreev Reflection


Nernst Equation (Electrode Potential)


Butler-Volmer Equation (Electrode Kinetics)


Tafel Equation (High Overpotential Limit)


Randles-Sevcik Equation (Cyclic Voltammetry Peak Current)


Cottrell Equation (Chronoamperometry)


Faraday's Laws of Electrolysis


Wagner Number (Current Distribution Uniformity)


Zener Anelasticity (Standard Linear Solid)


Debye Peak (Internal Friction, Point Defect Relaxation)


Bordoni Peak (Dislocation Relaxation)


Granato-Lücke Theory (Dislocation Damping)


Einstein Viscosity Equation (Rigid Sphere Suspension, Dilute)


Krieger-Dougherty Equation (Concentrated Suspension)


Frank-Oseen Free Energy (Liquid Crystal Elastic)


Frederiks Transition Threshold (Liquid Crystal)


Rayleigh Instability (Liquid Jet Breakup)


Plateau-Rayleigh Instability for Liquid Threads


Kissinger Equation (DSC/DTA Peak Kinetics)


Ozawa-Flynn-Wall Equation (Isoconversional Kinetics)


Tammann Nucleation Diagram (Nucleation vs Growth Rate)


Time-Temperature-Transformation (TTT) Diagram Equation


Thornton Structure Zone Model (Thin Film Growth)


Herring Scaling Laws (Sintering Kinetics)


Pilling-Bedworth Ratio (Oxide Protectiveness)


Ellingham Diagram (Oxide Thermodynamic Stability)


Mott-Gurney Law (Space-Charge-Limited Current)


Richardson-Dushman Equation (Thermionic Emission)


Schottky Barrier Height (Metal-Semiconductor)


Spicer's Unified Defect Model (Fermi Level Pinning at Interfaces)


Wolff's Law (Bone Remodeling, Mechanical Adaptation)


Fung's Quasi-Linear Viscoelasticity (Soft Tissue)


Ogden Hyperelastic Model (Biological Tissue)


Matthiessen's Rule (Electrical Resistivity Additivity)


Nordheim's Rule (Alloy Resistivity)


Miedema's Rules (Alloy Formation Enthalpy)


Köhler's Rule (Magnetoresistance Scaling)


Zener Breakdown (Band-to-Band Tunneling)


Klemens Model (Thermal Boundary Resistance / Kapitza)


Diffuse Mismatch Model (Thermal Boundary Resistance)