Physics Equation to LaTeX Converter

Convert physics equations from plain text or symbolic notation to proper LaTeX/KaTeX syntax for the FísicaFans blog.

Instructions

•Identify the equation type: Determine if it's inline math ($...$) or block/display math ($$...$$)
•Convert symbols: Replace plain text with proper LaTeX commands
•Structure: Use correct grouping, fractions, subscripts, superscripts
•Verify: Ensure KaTeX compatibility (subset of LaTeX)
•Test syntax: Check for proper escaping and balanced delimiters

Inline vs Block Math

Inline math - Within a paragraph:

markdown

La energía de un fotón es $E = h\nu$ donde $h$ es la constante de Planck.

Block math - Centered, separate line:

markdown

La ecuación de Schrödinger dependiente del tiempo:

$$
i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat{H}\Psi(\mathbf{r},t)
$$

Common Physics Equations

Classical Mechanics

Concept	Plain Text	LaTeX
Newton's 2nd Law	F = ma	$F = ma$
Kinetic Energy	KE = (1/2)mv²	$E_k = \frac{1}{2}mv^2$
Momentum	p = mv	$\mathbf{p} = m\mathbf{v}$
Work	W = F·d	$W = \mathbf{F} \cdot \mathbf{d}$
Gravitational Force	F = G(m₁m₂)/r²	$F = G\frac{m_1 m_2}{r^2}$

Thermodynamics

Concept	Plain Text	LaTeX
First Law	ΔU = Q - W	$\Delta U = Q - W$
Ideal Gas Law	PV = nRT	$PV = nRT$
Entropy	ΔS = Q/T	$\Delta S = \frac{Q}{T}$
Carnot Efficiency	η = 1 - (Tc/Th)	$\eta = 1 - \frac{T_c}{T_h}$

Electromagnetism

Concept	Plain Text	LaTeX
Coulomb's Law	F = k(q₁q₂)/r²	$F = k\frac{q_1 q_2}{r^2}$
Electric Field	E = F/q	$\mathbf{E} = \frac{\mathbf{F}}{q}$
Ohm's Law	V = IR	$V = IR$
Magnetic Force	F = qvB sin(θ)	$F = qvB\sin\theta$
Maxwell's Equations	∇·E = ρ/ε₀	$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$

Quantum Mechanics

Concept	Plain Text	LaTeX
Energy Quantization	E = hν = ℏω	$E = h\nu = \hbar\omega$
de Broglie	λ = h/p	$\lambda = \frac{h}{p}$
Heisenberg Uncertainty	ΔxΔp ≥ ℏ/2	$\Delta x \Delta p \geq \frac{\hbar}{2}$
Wave Function	ψ(x,t) = A sin(kx - ωt)	$\psi(x,t) = A\sin(kx - \omega t)$
Schrödinger (time-independent)	Hψ = Eψ	$\hat{H}\psi = E\psi$

Relativity

Concept	Plain Text	LaTeX
Mass-Energy	E = mc²	$E = mc^2$
Lorentz Factor	γ = 1/√(1-v²/c²)	$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
Time Dilation	Δt' = γΔt	$\Delta t' = \gamma \Delta t$
Length Contraction	L = L₀/γ	$L = \frac{L_0}{\gamma}$
Spacetime Interval	(Δs)² = (cΔt)² - (Δx)²	$(\Delta s)^2 = (c\Delta t)^2 - (\Delta x)^2$

LaTeX Command Reference

Greek Letters

Symbol	Command	Symbol	Command
α	`\alpha`	Γ	`\Gamma`
β	`\beta`	Δ	`\Delta`
γ	`\gamma`	Θ	`\Theta`
δ	`\delta`	Λ	`\Lambda`
ε	`\varepsilon`	Σ	`\Sigma`
θ	`\theta`	Ω	`\Omega`
λ	`\lambda`	Φ	`\Phi`
μ	`\mu`	Ψ	`\Psi`
ν	`\nu`	π	`\pi`
ρ	`\rho`	τ	`\tau`
σ	`\sigma`	ω	`\omega`
φ	`\phi`	ℏ	`\hbar`

Mathematical Operators

Operation	Command	Example
Fraction	`\frac{num}{den}`	$\frac{a}{b}$
Square root	`\sqrt{x}`	$\sqrt{x^2 + y^2}$
Nth root	`\sqrt[n]{x}`	$\sqrt[3]{8}$
Superscript	`x^2`	$e^{i\pi}$
Subscript	`x_i`	$x_{i,j}$
Sum	`\sum_{i=1}^{n}`	$\sum_{i=1}^{n} x_i$
Integral	`\int_{a}^{b}`	$\int_{0}^{\infty} e^{-x}dx$
Partial derivative	`\frac{\partial f}{\partial x}`	$\frac{\partial^2 u}{\partial t^2}$
Vector	`\mathbf{v}`	$\mathbf{F} = m\mathbf{a}$
Hat (operator)	`\hat{H}`	$\hat{H}\psi$
Dot product	`\cdot`	$\mathbf{a} \cdot \mathbf{b}$
Cross product	`\times`	$\mathbf{a} \times \mathbf{b}$
Nabla	`\nabla`	$\nabla \times \mathbf{E}$

Spacing and Formatting

Command	Purpose	Example
`\,`	Small space	$a\,b$
`\quad`	Medium space	$a \quad b$
`\qquad`	Large space	$a \qquad b$
`\text{}`	Regular text	$E = mc^2 \text{ where } c \text{ is speed of light}$
`\left( \right)`	Auto-sized parentheses	$\left(\frac{a}{b}\right)^2$
`\begin{aligned}...\end{aligned}`	Multi-line equations	See below

Multi-line Equations

latex

$$
\begin{aligned}
E &= mc^2 \\
p &= \gamma mv \\
E^2 &= (pc)^2 + (mc^2)^2
\end{aligned}
$$

Common Mistakes to Avoid

•Missing delimiters: Always close $...$ or $$...$$
•Unescaped special characters: Use \{ \} \_ \% for literal characters
•Wrong quotes: Use ' for prime notation: $x'$
•Spacing in subscripts: x_12 vs x_{12} (different meanings)
•Operator precedence: Use {} to group: x^{2+3} not x^2+3

Conversion Workflow

When user provides an equation:

•Parse: Identify all mathematical symbols and structure
•Greek letters: Convert α, β, γ, etc. to \alpha, \beta, \gamma
•Subscripts/superscripts: Convert E₀ → E_0, x² → x^2
•Fractions: Convert / to \frac{numerator}{denominator}
•Special functions: sin, cos, log → \sin, \cos, \log
•Vectors: Add \mathbf{} for vector notation
•Test: Verify syntax is KaTeX-compatible

Example Conversions

Input: "The kinetic energy is KE = (1/2)mv² and momentum p = mv"

Output:

markdown

La energía cinética es $E_k = \frac{1}{2}mv^2$ y el momento lineal es $\mathbf{p} = m\mathbf{v}$.

Input: "Schrödinger equation: iℏ(∂ψ/∂t) = Hψ"

Output:

markdown

$$
i\hbar\frac{\partial\psi}{\partial t} = \hat{H}\psi
$$

Integration with MDX Posts

For physics blog posts, include equations naturally:

mdx

---
title: "Mecánica Cuántica: Fundamentos"
---

## La Ecuación de Schrödinger

La ecuación fundamental de la mecánica cuántica describe cómo evoluciona la función de onda $\psi$ en el tiempo:

$$
i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat{H}\Psi(\mathbf{r},t)
$$

Donde $\hbar = \frac{h}{2\pi}$ es la constante de Planck reducida y $\hat{H}$ es el operador Hamiltoniano.

Validation

Before finalizing, check:

•✅ Delimiters are balanced ($...$ or $$...$$)
•✅ Special characters are escaped (_, ^, {, }, \, etc.)
•✅ Greek letters use proper commands
•✅ Fractions use \frac{}{}
•✅ Vectors use \mathbf{}
•✅ Operators use \hat{} when appropriate
•✅ Syntax is KaTeX-compatible (no advanced LaTeX packages)

Reference

For complete equation list, see common-equations.md.