How to denote laplacian operator(∇²) in LaTeX?

Laplacian or Laplace operator is a differential operator, denoted by the square of dell operator(∇²).

In latex, the Laplacian operator is represented by \nabla^{2} command syntax.

\documentclass{article}
\begin{document}
  $$ \nabla^{2} $$
\end{document}

Output :

laplacian operator symbol

And the Laplacian operator is expressed in the form of a dot product of two gradient operators. For example

\documentclass{article}
\begin{document}
  $$\nabla^{2}=\vec{\nabla}\cdot\vec{\nabla}$$
  $$\nabla^{2}=\frac{\partial^2 }{\partial x^2}+\frac{\partial^2 }{\partial y^2}+\frac{\partial^2 }{\partial z^2}$$
\end{document}

Output :

laplacial symbol form of dot product

The best practice is to install the physics package to identify the Laplacian operator in the best way because the physics package contains the predetermined \laplacian command to represent this operator.

\documentclass{article}
\usepackage{physics}
\begin{document}
 $$ \laplacian  $$
 $$ \laplacian{f} $$
 $$ \laplacian(f_{1}+f_{2}) $$
 $$ \laplacian[f_{1}+f_{2}+\cdots+f_{n}] $$
\end{document}

Output :

laplacian operation with physics package in LaTeX

In latex, nabla symbol of the laplacian operation cannot be in a bold format or a vector arrow mark above the symbol. Because this operator is a scalar operator.

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