Undergrad Vector calculus identity format question

[kent davidge]

I know there is an identity involving the Laplacian that is like $\nabla^2 \vec A = \nabla^2 A$ where $\vec A$ is a vector and $A$ is its magnitude, but can't remember the correct form. Does anyone knows it?

 

[jedishrfu]

There's the vector laplacian:

https://en.wikipedia.org/wiki/Vector_Laplacian

and the scalar laplacian:

http://hyperphysics.phy-astr.gsu.edu/hbase/lapl.html

 

[Haborix]

If you were so inclined you could set $\vec{A}=|\vec{A}|\hat{n}$, then churn out how the Laplacian looks in terms of various derivatives of $|\vec{A}|$ and $\hat{n}$. I don't think you will get anything pretty.

 

[jedishrfu]

There's a vector identity with the vector laplacian here:

https://mathworld.wolfram.com/VectorLaplacian.html