4.2. Latex Basics

last update: Feb 07, 2024

4.2.1. Inline equations

You can write inline equations by using $.

Example

The equation $E=mc^2$ is the most famous equation in physics.

The equation \(E=mc^2\) is the most famous equation in physics.

4.2.2. Display equations

You can write display equations by using $$ or \[ \].

Example

Schrodinger equation:
$$
    i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle = H |\psi(t)\rangle
$$

Schrodinger equation:

\[ i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle = H |\psi(t)\rangle \]

Tip

You can use shorter commands with physics package.

\begin{align}
   i\hbar\pdv{t} \ket{\psi(t)} = H \ket{\psi(t)}
\end{align}

\[\begin{align} i\hbar\pdv{t} \ket{\psi(t)} = H \ket{\psi(t)} \end{align}\]

4.2.3. Basic Symbols

Greek letters

Command	Symbol
\alpha	\(\alpha\)
\beta	\(\beta\)
\gamma	\(\gamma\)
\delta	\(\delta\)
\epsilon	\(\epsilon\)
\zeta	\(\zeta\)
\eta	\(\eta\)
\theta	\(\theta\)
\iota	\(\iota\)
\kappa	\(\kappa\)
\lambda	\(\lambda\)
\mu	\(\mu\)
\nu	\(\nu\)
\xi	\(\xi\)
\pi	\(\pi\)
\rho	\(\rho\)
\sigma	\(\sigma\)
\tau	\(\tau\)
\upsilon	\(\upsilon\)
\phi	\(\phi\)
\chi	\(\chi\)
\psi	\(\psi\)
\omega	\(\omega\)
\Gamma	\(\Gamma\)
\Delta	\(\Delta\)
\Theta	\(\Theta\)
\Lambda	\(\Lambda\)
\Xi	\(\Xi\)
\Pi	\(\Pi\)
\Sigma	\(\Sigma\)
\Upsilon	\(\Upsilon\)
\Phi	\(\Phi\)
\Psi	\(\Psi\)
\Omega	\(\Omega\)

Operators

Command	Symbol
+	\(+\)
-	\(-\)
=	\(=\)
\div	÷
\frac{a}{b}	\(\frac{a}{b}\)
\times	\(\times\)
\pm	\(\pm\)

Note

In physics package, \div is replaced by \(\nabla\cdot\)

Big Operators

Command	Symbol
\lim x	\(\lim x\)
\lim_{x \to \infty} x	\(\lim_{x \to \infty} x\)
\lim\limits_{x \to \infty} x	\(\lim\limits_{x \to \infty} x\)
\sum x	\(\sum x\)
\sum_{i=1}^n x	\(\sum_{i=1}^n x\)
\sum\limits_{i=1}^n x	\(\sum\limits_{i=1}^n x\)
\prod_{i=1}^n x	\(\prod_{i=1}^n x\)
\coprod_{i=1}^n x	\(\coprod_{i=1}^n x\)
\bigcup_{i=1}^n x	\(\bigcup_{i=1}^n x\)
\bigcap_{i=1}^n x	\(\bigcap_{i=1}^n x\)
\bigvee_{i=1}^n x	\(\bigvee_{i=1}^n x\)
\bigwedge_{i=1}^n x	\(\bigwedge_{i=1}^n x\)
\bigsqcup_{i=1}^n x	\(\bigsqcup_{i=1}^n x\)
\bigodot_{i=1}^n x	\(\bigodot_{i=1}^n x\)
\bigotimes_{i=1}^n x	\(\bigotimes_{i=1}^n x\)
\int_a^b x	\(\int_a^b x\)
\oint_a^b x	\(\oint_a^b x\)
\iint_a^b x	\(\iint_a^b x\)
\iiint_a^b x	\(\iiint_a^b x\)

Miscellaneous

Command	Symbol
\forall	\(\forall\)
\exists	\(\exists\)
\partial	\(\partial\)
\nabla	\(\nabla\)
\infty	\(\infty\)
\dots	\(\dots\)
\cdot	\(\cdot\)
\cdots	\(\cdots\)
\vdots	\(\vdots\)
\ddots	\(\ddots\)
\therefore	\(\therefore\)
\because	\(\because\)
\clubsuit	\(\clubsuit\)
\diamondsuit	\(\diamondsuit\)
\heartsuit	\(\heartsuit\)
\spadesuit	\(\spadesuit\)
\prime	\(\prime\)
f^\prime	\(f^\prime\)
\angle	\(\angle\)

Dots

\[ \sum_{i=1}^n x_i = x_1 + x_2 + \cdots + x_n \]

\[\begin{split} A = \mqty[a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{n1} & \cdots & a_{nn}] \end{split}\]

Functions

Command	Symbol
\sqrt{x}	\(\sqrt{x}\)
\sqrt[n]{x}	\(\sqrt[n]{x}\)
\sin x	\(\sin x\)
\cos x	\(\cos x\)
\tan x	\(\tan x\)
\cot x	\(\cot x\)
\sec x	\(\sec x\)
\csc x	\(\csc x\)
\arcsin x	\(\arcsin x\)
\arccos x	\(\arccos x\)
\arctan x	\(\arctan x\)
\sinh x	\(\sinh x\)
\cosh x	\(\cosh x\)
\tanh x	\(\tanh x\)
\coth x	\(\coth x\)
\log x	\(\log x\)
\ln x	\(\ln x\)
\exp x	\(\exp x\)
\binom{n}{k}	\(\binom{n}{k}\)

Tip

You can wirte \sum\limits_{i=1}^n x instead of \sum_{i=1}^n x to make the limits appear above and below the symbol.

You can wirte \(\sum\limits_{i=1}^n x\) instead of \(\sum_{i=1}^n x\) to make the limits appear above and below the symbol.

Relations

Command	Symbol
a = b	\(a = b\)
a \neq b	\(a \neq b\)
a \approx b	\(a \approx b\)
a \equiv b	\(a \equiv b\)
a \leq b	\(a \leq b\)
a \geq b	\(a \geq b\)
a \ll b	\(a \ll b\)
a \gg b	\(a \gg b\)
a \sim b	\(a \sim b\)
a \propto b	\(a \propto b\)
a \subset b	\(a \subset b\)
a \supset b	\(a \supset b\)
a \subseteq b	\(a \subseteq b\)
a \supseteq b	\(a \supseteq b\)
a \in b	\(a \in b\)
a \ni b	\(a \ni b\)
a \notin b	\(a \notin b\)
a \mapsto b	\(a \mapsto b\)
a \to b	\(a \to b\)
a \gets b	\(a \gets b\)
a \leftrightarrow b	\(a \leftrightarrow b\)
a \Leftrightarrow b	\(a \Leftrightarrow b\)
a \implies b	\(a \implies b\)
a \impliedby b	\(a \impliedby b\)
a \iff b	\(a \iff b\)
a \to b	\(a \to b\)
a \gets b	\(a \gets b\)
a \uparrow b	\(a \uparrow b\)
a \downarrow b	\(a \downarrow b\)
a \updownarrow b	\(a \updownarrow b\)
a \Uparrow b	\(a \Uparrow b\)
a \Downarrow b	\(a \Downarrow b\)
a \Updownarrow b	\(a \Updownarrow b\)
a \mid b	\(a \mid b\)
a \parallel b	\(a \parallel b\)
a \perp b	\(a \perp b\)
a \smile b	\(a \smile b\)
a \frown b	\(a \frown b\)
a \vdash b	\(a \vdash b\)
a \dashv b	\(a \dashv b\)

Spaces

Command	Symbol
a \! b	\(a \! b\)
a \, b	\(a \, b\)
a \: b	\(a \: b\)
a \; b	\(a \; b\)
a \hspace{1pt} b	\(a \hspace{1pt} b\)
a \hspace{1mm} b	\(a \hspace{1mm} b\)
a \hspace{1ex} b	\(a \hspace{1ex} b\)
a \hspace{1em} b	\(a \hspace{1em} b\)
a \quad b	\(a \quad b\)
a \qquad b	\(a \qquad b\)
a \hspace{1cm} b	\(a \hspace{1cm} b\)
a \hspace{1in} b	\(a \hspace{1in} b\)

Brackets and Parentheses

Command	Symbol
$(A)$	\((A)\)
$[A]$	\([A]\)
$\{A\}$	\(\{A\}\)
$\langle A \rangle$	\(\langle A \rangle\)
$\vert A \vert$	\(\vert A \vert\)
$\Vert A \Vert$	\(\Vert A \Vert\)
$\lfloor A \rfloor$	\(\lfloor A \rfloor\)
$\lceil A \rceil$	\(\lceil A \rceil\)

Accents

Command	Symbol
\hat{a}	\(\hat{a}\)
\check{a}	\(\check{a}\)
\tilde{a}	\(\tilde{a}\)
\acute{a}	\(\acute{a}\)
\grave{a}	\(\grave{a}\)
\dot{a}	\(\dot{a}\)
\ddot{a}	\(\ddot{a}\)
\breve{a}	\(\breve{a}\)
\bar{a}	\(\bar{a}\)
\vec{a}	\(\vec{a}\)

Styles

Command	Example
\mathit{A}	\(\mathit{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}\)
\mathrm{A}	\(\mathrm{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}\)
\mathsf{A}	\(\mathsf{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}\)
\mathbf{A}	\(\mathbf{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}\)
\mathcal{A}	\(\mathcal{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}\)
\mathfrak{A}	\(\mathfrak{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}\)
\mathbb{A}	\(\mathbb{A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z}\)

Matrices

Symbol	Command
\begin{pmatrix} a \\ b \end{pmatrix}	\(\begin{pmatrix} a \\ b \end{pmatrix}\)
\begin{pmatrix} a & b \\ c & d \end{pmatrix}	\(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)
\begin{bmatrix} a & b \\ c & d \end{bmatrix}	\(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\)
\begin{vmatrix} a & b \\ c & d \end{vmatrix}	\(\begin{vmatrix} a & b \\ c & d \end{vmatrix}\)
\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}	\(\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}\)

4.2.4. amsmath package

You can use amsmath package to use more commands, such as cases and align.

cases

You can use cases environment to write piecewise functions.

\begin{align}
   f(x) = \begin{cases}
       0 & (x < 0) \\
       1 & (x \geq 0)
   \end{cases}
\end{align}

\[\begin{split}\begin{align} f(x) = \begin{cases} 0 & (x < 0) \\ 1 & (x \geq 0) \end{cases} \end{align}\end{split}\]

align

You can align equations by using align environment. You can align equations by &.

\begin{align}
   f(x) &= \int_{0}^{x} \left( \frac{1}{2}t^3 - 3t^2 + 4t + 7 \right) dt \\
   &= \left[ \frac{1}{8}t^4 - t^3 + 2t^2 + 7t \right]_{0}^{x} \\
   &= \frac{1}{8}x^4 - x^3 + 2x^2 + 7x
\end{align}

\[\begin{split}\begin{align} f(x) &= \int_{0}^{x} \left( \frac{1}{2}t^3 - 3t^2 + 4t + 7 \right) dt \\ &= \left[ \frac{1}{8}t^4 - t^3 + 2t^2 + 7t \right]_{0}^{x} \\ &= \frac{1}{8}x^4 - x^3 + 2x^2 + 7x \end{align}\end{split}\]

4.2.5. physics package

You can use physics package to use more commands, such as \qty, \dv, pdv, \eval, \order, \abs, \norm, \commutator [or \comm], \anticommutator [or \acomm]

\qty

You can use \qty command to write adaptive parentheses instead of \left and \right.

\begin{align}
   \qty( \frac{1}{2} )
   \quad
   \qty[ \frac{1}{2} ]
   \quad
   \qty{ \frac{1}{2} }
\end{align}

\[\begin{align} \qty( \frac{1}{2} ) \quad \qty[ \frac{1}{2} ] \quad \qty{ \frac{1}{2} } \end{align}\]

dv

You can use dv command to write derivatives easily.

\begin{align}
   \dv{x} \sin{x} = \cos{x}
\end{align}

\[\begin{align} \dv{x} \sin{x} = \cos{x} \end{align}\]

pdv

You can use pdv command to write partial derivatives easily.

\begin{align}
   \pdv{x} f(x, y), \quad \pdv{f}{x}, \quad \pdv{f}{x}{y}, \quad \pdv[2]{f}{x}
\end{align}

\[\begin{align} \pdv{x} f(x, y), \quad \pdv{f}{x}, \quad \pdv{f}{x}{y}, \quad \pdv[2]{f}{x} \end{align}\]

\eval

You can use \eval command to write evaluation easily.

\begin{align}
   \eval{x^2}_{x=1}, \quad \eval{x^{-2}}_{1}^{\infty}
\end{align}

\[\begin{align} \eval{x^2}_{x=1}, \quad \eval{x^{-2}}_{1}^{\infty} \end{align}\]

\order

You can use \order command to write order easily.

\begin{align}
   \order{x^2}, \quad \order{\frac{1}{x^2}}
\end{align}

\[\begin{align} \order{x^2}, \quad \order{\frac{1}{x^2}} \end{align}\]

\abs

You can use \abs command to write absolute value easily.

\begin{align}
   \abs{x}, \quad \abs{\frac{1}{x}}
\end{align}

\[\begin{align} \abs{x}, \quad \abs{\frac{1}{x}} \end{align}\]

\norm

You can use \norm command to write norm easily.

\begin{align}
   \norm{x}, \quad \norm{\frac{1}{x}}
\end{align}

\[\begin{align} \norm{x}, \quad \norm{\frac{1}{x}} \end{align}\]

\commutator [or \comm]

You can use \commutator command to write commutator easily.

\begin{align}
   \commutator{A}{B}, \quad \comm{A}{B}
\end{align}

\[\begin{align} \commutator{A}{B}, \quad \comm{A}{B} \end{align}\]

\anticommutator [or \acomm]

You can use \anticommutator command to write anticommutator easily.

\begin{align}
   \anticommutator{A}{B}, \quad \acomm{A}{B}
\end{align}

\[\begin{align} \anticommutator{A}{B}, \quad \acomm{A}{B} \end{align}\]

Vector notation

Command	Output
\va{a}	\(\va{a}\)
\vb{a}	\(\vb{a}\)
\grad{a}	\(\grad{a}\)
\curl{a}	\(\curl{a}\)
\div{a}	\(\div{a}\)
\laplacian{a}	\(\laplacian{a}\)

Operators

Command	Output
\tr[A]	\(\tr[A]\)
\Tr[A]	\(\Tr[A]\)
\rank M	\(\rank M\)
\erf	\(\erf\)
\Res	\(\Res\)
\pv{\int f(z) \dd{z}}	\(\pv{\int f(z) \dd{z}}\)
\Re	\(\Re\)
\Im	\(\Im\)

Dirac bra-ket notation

Command	Output
\ket{a}	\(\ket{a}\)
\bra{a}	\(\bra{a}\)
\braket{a}	\(\braket{a}\)
\braket{a}{b}	\(\braket{a}{b}\)
dyad{a}	\(\dyad{a}\)
dyad{a}{b}	\(\dyad{a}{b}\)
expval{A}	\(\expval{A}\)
ev{A}	\(\ev{A}\)
expval{A}{a}	\(\expval{A}{a}\)
ev{A}{a}	\(\ev{A}{a}\)
\mel{a}{A}{b}	\(\mel{a}{A}{b}\)

Matrices

Command	Output
\mqty(a & b \\ c & d)	\(\mqty(a & b \\ c & d)\)
\mqty[ a & b \\ c & d ]	\(\mqty[ a & b \\ c & d ]\)
\vmqty{a & b \\ c & d}	\(\vmqty{a & b \\ c & d}\)
\mqty[\imat{2}]	\(\mqty[\imat{2}]\)
\mqty[\pmat{0}]	\(\mqty[\pmat{0}]\)
\mqty[\pmat{1}]	\(\mqty[\pmat{1}]\)
\mqty[\pmat{2}]	\(\mqty[\pmat{2}]\)
\mqty[\pmat{3}]	\(\mqty[\pmat{3}]\)
\mqty(\dmat{1,2,3})	\(\mqty(\dmat{1,2,3})\)
\mqty(\admat{1,2,3})	\(\mqty(\admat{1,2,3})\)