The 30 Most Important Equations in Physics - ChatGPT

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Concepts

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