# Correct symbol for the Laplace operator ($\Delta$)

What is the correct symbol to use for the Laplace operator? It looks almost like the big Delta $\Delta$, but it should look different so that it is not confused with the Delta.

Currently, I use $\vec \nabla^2$, which is unambiguous, but not pretty.

• According to the Comprehensive LaTeX Symbol List \Delta is used for it. See page 50. Oct 13 '12 at 18:07
• Also, the only symbol used on Wikipedia - the source of all knowledge - is \Delta (apart from \mathcal{L}). :) Oct 13 '12 at 18:16
• Link to Comprehensive LaTeX Symbol List. See page 50. Oct 13 '12 at 18:17
• don't you mean page 150, @azetina? Page 50 has only arrows.
– c.p.
Oct 13 '12 at 18:22
• Even if they look different, they will be confused. Don't use them with different meanings! (The same applies, e.g., to \epsilon and \varepsilon.) Oct 13 '12 at 19:23

If you use the D'Alembert operator as well, you might find pretty using the symbol \bigtriangleup for your Laplace operator, in order to get a similar look as the \Box symbol that is being used for D'Alambertian. In the following, a tricky construction with \mathop and \mathbin is used to get the proper spacing:

\documentclass{article}

\usepackage{amsmath,amssymb}

\newcommand*\Laplace{\mathop{}\!\mathbin\bigtriangleup}
\newcommand*\DAlambert{\mathop{}\!\mathbin\Box}

\pagestyle{empty}

\begin{document}

\begin{gather*}
\phi(1+\Laplace A) \neq \phi(1+\Delta A)
\\
\phi(1+\DAlambert A) \neq \phi(1+\Laplace A)
\\
f\Laplace g
\end{gather*}

\end{document} • I'd use \mathop{{}\bigtriangleup}\nolimits and \mathop{{}\Box}\nolimits which would ensure correct spacing in all situations. The {} is in order to avoid centering the operator with respect to the formula axis. Oct 13 '12 at 21:15
• The d'Alambert operator will come eventually since I am a physicist. I like your solution, since it looks consistent. Oct 14 '12 at 14:29
• What does the !\mathbin-part actually do ? And how would you make \bigtriangledown look like \nabla (in terms of vertical spacing) ? Aug 6 '17 at 17:09
• @hillbilly To provide the asymetric spacing in the third example.
– yo'
Aug 7 '17 at 22:38
• Just for the record: the combination “Op-Bin” is impossible (table on page 170 of the TeXbook), so the \mathbin does nothing at all, because \mathbin\Box is eventually treated as an Ord atom. The “asymmetry” in the third example is due to the fact that the atoms are “Ord-Op-(Bin->Ord)-Ord”. The space is created by the first two atoms. May 30 '18 at 8:52

The operator is defined, in the international standard ISO 80000-1, as identified with the Unicode character U+2206 INCREMENT (mistakenly called DELTA in the standard), which has “Laplace operator” as one of its alias names. Thus, it is regarded as distinct from the Greek capital letter delta U+0394. This is however a logical, character-level distinction and does not imply that different glyphs must be used. On the other hand, many fonts make a distinction, sometimes very small, sometimes quite noticeable.

It seems to me that to make the difference in LaTeX, you would need to use a package that lets you enter a character by its Unicode number or enter Unicode characters as such. Along that second option, the following code seems to produce different renderings:

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{XITS Math}
\begin{document}
U+2206: $∆$

U+0394: $Δ$
\end{document} • I've taken the liberty of modifying your example; first to use XITS Math which is the same as STIXGeneral, but doesn't raise warnings when used as a math font. The other change is for making clear what Unicode character produces each glyph. Oct 13 '12 at 21:19
• @egreg: Could you please add a possibility to define a command for the "U+2206". I would like to get a "\laplace" working with lualatex and \usepackage[math-style=ISO]{unicode-math}. Thanks! Sep 2 '13 at 15:31
• @LaRiFaRi The symbol is called \increment with unicode-math. If you want \laplace to use it, just do \newcommand{\laplace}{\increment} Sep 2 '13 at 15:40
• It seems that unfortunately the package unicode-math requires one of the compilers xelatex or Lualatex. Oct 30 '13 at 14:58

According to the Comprehensive LaTeX Symbol List one can use the symbol \Delta and corresponding \nabla to represent the Laplace operator. I don't know if \Updelta is a possibility from  txfonts/pxfonts.

There is another way to display the Laplacian. I found it in accident.

\mathcal{4}

So you can also define

\newcommand*\laplace{\mathop{}\!\mathcal{4}}

• this though depends on the (limitation of) certain font engines, and you should not rely on this . E.g. when using the package unicode-math (see above) \mathcal{4} will print 4
– am70
Nov 29 '19 at 12:42