The 30 Most Important Equations in Physics - ChatGPT

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Concepts

id	yearAppeared	creditedTo	country	applications	fieldOfPhysics	complexity	equation
Newton's Second Law	1687	Isaac Newton	England	100	Mechanics	2	F = ma
Einstein's Mass-Energy Equivalence	1905	Albert Einstein	Switzerland	50	Relativity	5	E = mc^2
Schrödinger Equation	1926	Erwin Schrödinger	Austria	100	Quantum Mechanics	7	i\hbar\frac{\partial}{\partial t}\psi = \hat{H}\psi
Maxwell's Equations	1865	James Clerk Maxwell	Scotland	50	Electromagnetism	6	\begin{align} \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{align}
Boltzmann Equation	1872	Ludwig Boltzmann	Austria	30	Statistical Mechanics	8	\frac{\partial f}{\partial t} + \mathbf{v} \cdot \nabla f + \mathbf{a} \cdot \frac{\partial f}{\partial \mathbf{v}} = \left( \frac{\partial f}{\partial t} \right)_\text{collision}
Planck's Equation	1900	Max Planck	Germany	40	Quantum Mechanics	6	E = h\nu
Heisenberg Uncertainty Principle	1927	Werner Heisenberg	Germany	20	Quantum Mechanics	5	\Delta x \Delta p \geq \frac{\hbar}{2}
Hubble's Law	1929	Edwin Hubble	USA	25	Cosmology	4	v = H_0 d
Fourier Transform	1822	Joseph Fourier	France	70	Mathematical Physics	6	\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i x \xi} \, dx
Lorentz Transformation	1904	Hendrik Lorentz	Netherlands	20	Relativity	6	\begin{align} t' &= \gamma \left( t - \frac{vx}{c^2} \right) \\ x' &= \gamma (x - vt) \end{align}
Dirac Equation	1928	Paul Dirac	UK	30	Quantum Mechanics	9	\left( i\gamma^\mu \partial_\mu - m \right) \psi = 0
Navier-Stokes Equation	1822	Claude-Louis Navier, George Gabriel Stokes	France, UK	50	Fluid Mechanics	9	\rho \left( \frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u} \right) = -\nabla p + \mu \nabla^2 \mathbf{u} + \mathbf{f}
Ohm's Law	1827	Georg Ohm	Germany	100	Electromagnetism	2	V = IR
Hooke's Law	1678	Robert Hooke	England	60	Mechanics	2	F = -kx
Kepler's Third Law	1619	Johannes Kepler	Germany	30	Astronomy	3	T^2 \propto r^3
Bernoulli's Principle	1738	Daniel Bernoulli	Switzerland	50	Fluid Mechanics	4	p + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}
Faraday's Law of Induction	1831	Michael Faraday	England	40	Electromagnetism	5	\mathcal{E} = -\frac{d\Phi_B}{dt}
Stefan-Boltzmann Law	1879	Josef Stefan, Ludwig Boltzmann	Austria	30	Thermodynamics	5	j^* = \sigma T^4
Lenz's Law	1834	Heinrich Lenz	Russia	30	Electromagnetism	4	\mathcal{E} = -\frac{d\Phi_B}{dt}
Coulomb's Law	1785	Charles-Augustin de Coulomb	France	50	Electrostatics	3	F = k_e \frac{q_1 q_2}{r^2}
Fermi-Dirac Statistics	1926	Enrico Fermi, Paul Dirac	Italy, UK	40	Quantum Mechanics	7	f(E) = \frac{1}{e^{(E - \mu)/kT} + 1}
Bose-Einstein Statistics	1924	Satyendra Nath Bose, Albert Einstein	India, Germany	30	Quantum Mechanics	7	f(E) = \frac{1}{e^{(E - \mu)/kT} - 1}
Wien's Displacement Law	1893	Wilhelm Wien	Germany	25	Thermodynamics	5	\lambda_\text{peak} T = b
Poisson's Equation	1813	Siméon Denis Poisson	France	30	Mathematical Physics	6	\nabla^2 \phi = -\frac{\rho}{\epsilon_0}
Ampère's Law	1826	André-Marie Ampère	France	40	Electromagnetism	4	\nabla \times \mathbf{B} = \mu_0 \mathbf{J}
Biot-Savart Law	1820	Jean-Baptiste Biot, Félix Savart	France	30	Electromagnetism	5	d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{\hat{r}}}{r^2}
Kirchhoff's Circuit Laws	1845	Gustav Kirchhoff	Germany	50	Electrical Circuits	3	\begin{align} \sum I = 0 \\ \sum V = 0 \end{align}
Gibbs Free Energy	1873	Josiah Willard Gibbs	USA	30	Thermodynamics	6	G = H - TS
Avogadro's Law	1811	Amedeo Avogadro	Italy	30	Chemistry	3	V \propto n
de Broglie Hypothesis	1924	Louis de Broglie	France	25	Quantum Mechanics	6	\lambda = \frac{h}{p}