Learn how to typeset physics equations, symbols, and notation professionally in LaTeX.
Essential Physics Packages
\usepackage{amsmath} % Essential math
\usepackage{amssymb} % Extra symbols
\usepackage{physics} % Physics shortcuts
\usepackage{siunitx} % SI units
\usepackage{tensor} % Tensor notation
\usepackage{braket} % Quantum mechanics
Common Physics Symbols
| Symbol | LaTeX | Description |
|---|
| ℏ | \hbar | Reduced Planck constant |
| ∇ | \nabla | Gradient/Del operator |
| ∂ | \partial | Partial derivative |
| ∞ | \infty | Infinity |
| · | \cdot | Dot product |
| × | \times | Cross product |
| ⊗ | \otimes | Tensor product |
| ∑ | \sum | Summation |
| ∫ | \int | Integral |
| ∮ | \oint | Closed integral |
Vectors and Tensors
Vector Notation
% Different vector styles
\vec{F} = m\vec{a} % Arrow notation
\mathbf{F} = m\mathbf{a} % Bold notation
\boldsymbol{\tau} = \vec{r} \times \vec{F} % Bold Greek
% Vector operations
\vec{A} \cdot \vec{B} % Dot product
\vec{A} \times \vec{B} % Cross product
|\vec{v}| \text{ or } \|\vec{v}\| % Magnitude
% Unit vectors
\hat{i}, \hat{j}, \hat{k} % Cartesian
\hat{r}, \hat{\theta}, \hat{\phi} % Spherical
\vec{F} → F (vector)
\vec{A} \cdot \vec{B} → A · B (dot product)
\vec{A} \times \vec{B} → A × B (cross product)
\hat{i}, \hat{j}, \hat{k} → i, j, k (unit vectors)
Tensor Notation
% Tensor indices
T^{\mu\nu} % Contravariant
T_{\mu\nu} % Covariant
T^{\mu}_{\nu} % Mixed
% Einstein notation
g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}
% Christoffel symbols
\Gamma^{\lambda}_{\mu\nu}
% Riemann tensor
R^{\rho}_{\sigma\mu\nu}
Quantum Mechanics
Bra-Ket Notation
% Basic bra-ket
\ket{\psi} % Ket
\bra{\phi} % Bra
\braket{\phi|\psi} % Inner product
\braket{\phi|H|\psi} % Matrix element
% Operators
\hat{H}\ket{\psi} = E\ket{\psi} % Eigenvalue equation
\hat{p} = -i\hbar\frac{\partial}{\partial x}
% Commutators
[\hat{x}, \hat{p}] = i\hbar
\{\hat{a}, \hat{a}^{\dagger}\} = 1 % Anticommutator
Wave Functions
% Schrödinger equation
i\hbar\frac{\partial}{\partial t}\Psi = \hat{H}\Psi
% Plane wave
\psi(x,t) = Ae^{i(kx - \omega t)}
% Spherical harmonics
Y_{\ell}^m(\theta, \phi)
% Probability density
|\psi(x,t)|^2 = \psi^*(x,t)\psi(x,t)
Classical Mechanics
Lagrangian and Hamiltonian
% Lagrangian
L = T - V = \frac{1}{2}m\dot{x}^2 - V(x)
% Euler-Lagrange equation
\frac{d}{dt}\frac{\partial L}{\partial \dot{q}} - \frac{\partial L}{\partial q} = 0
% Hamiltonian
H = \sum_i p_i\dot{q}_i - L
% Hamilton's equations
\dot{q}_i = \frac{\partial H}{\partial p_i}, \quad
\dot{p}_i = -\frac{\partial H}{\partial q_i}
Electromagnetism
Maxwell’s Equations
% Differential form
\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}
\nabla \cdot \vec{B} = 0
\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}
\nabla \times \vec{B} = \mu_0\vec{J} + \mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}
% Integral form
\oint_S \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\epsilon_0}
\oint_C \vec{E} \cdot d\vec{\ell} = -\frac{d\Phi_B}{dt}
Field Notation
% Electromagnetic tensor
F^{\mu\nu} = \partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}
% Four-potential
A^{\mu} = (\phi/c, \vec{A})
% Lorentz force
\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})
Thermodynamics
Thermodynamic Relations
% First law
dU = \delta Q - \delta W = TdS - PdV
% Partial derivatives
\left(\frac{\partial U}{\partial S}\right)_V = T
\left(\frac{\partial U}{\partial V}\right)_S = -P
% Maxwell relations
\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V
Units and Constants
SI Units with siunitx
% Basic units
\SI{3e8}{m/s} % Speed of light
\SI{6.626e-34}{J.s} % Planck constant
\SI{9.81}{m/s^2} % Acceleration
% Complex units
\SI{13.6}{eV} % Energy
\SI{2.5}{kg.m/s} % Momentum
\SI{1.23e-4}{N.m} % Torque
% Uncertainties
\SI{9.81 \pm 0.02}{m/s^2}
Special Relativity
Four-Vectors and Metrics
% Four-vectors
x^{\mu} = (ct, \vec{x})
p^{\mu} = (E/c, \vec{p})
% Minkowski metric
\eta_{\mu\nu} = \text{diag}(1, -1, -1, -1)
% Lorentz transformation
x'^{\mu} = \Lambda^{\mu}_{\nu} x^{\nu}
% Invariant interval
ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2
Tips for Physics Documents
Use Consistent Notation
Stick to either arrows or bold for vectors throughout your document
Define Your Symbols
Always define non-standard symbols when first introduced
Group Related Equations
Use align environments for related equations
Number Important Equations
Only number equations you reference later
Common Physics Environments
% For derivations
\begin{align}
F &= ma \\
&= m\frac{dv}{dt} \\
&= \frac{dp}{dt}
\end{align}
% For definitions
\begin{equation}
\boxed{E = mc^2}
\end{equation}
% For multiple cases
\begin{cases}
\psi(x) = Ae^{ikx} + Be^{-ikx} & \text{for } x < 0 \\
\psi(x) = Ce^{-\kappa x} & \text{for } x > 0
\end{cases}
Pro tip: The physics package provides many shortcuts like \dv{f}{x} for derivatives and \abs{\psi} for absolute values.
Further Reading
