Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs

Dashboard
Notifications
Mark all as read
Q&A

What does Laplace operator represent?

+1
−0

I was wondering what's the physical meaning of Laplace operator. $\vec\nabla$ actually represent a field. I had seen that Laplace operator is written as $\vec \nabla \cdot \vec\nabla=\nabla^2=\Delta$ So Laplace operator is scalar quantity. I had found usage of Laplace operator in a book and Wiki-page.

I think the laplace operator is also representing "field" but it works like Wave. In a book I had seen that $$\nabla^2\vec A=\frac{1}{v^2}\frac{\partial^2 \vec A}{\partial t^2}$$

The above equation is representing wave. So does that mean Laplace operator represents wave?

Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

1 comment thread

Interpretations of the Laplacian (1 comment)

1 answer

+0
−0

Laplacian acts like Divergence but not completely. If you take a function (called $\vec{A}$) and write that laplacian of that function is $0$ than it will be flat space.

$$\nabla^2\vec{A}=0$$

But if you write Laplacian like this :

$$\Delta \vec{A}=\text{c}\frac{\partial^2 \vec A}{\partial t^2}$$

than it will represent a wave.

Divergence of gradient actually means "changes in field with respect to that field".

In short we can say that Laplacian represent curvature or stress of the field.

Why does this post require moderator attention?
You might want to add some details to your flag.

0 comment threads

Sign up to answer this question »

This community is part of the Codidact network. We have other communities too — take a look!

You can also join us in chat!

Want to advertise this community? Use our templates!

Like what we're doing? Support us! Donate