Message Boards Message Boards

0
|
1054 Views
|
3 Replies
|
1 Total Likes
View groups...
Share
Share this post:

Integral in two dimensions

Posted 5 months ago

Reading a scientific article, I came across the following integral $$ \int_0^1 dx \int\dfrac{d^2\vec{k}}{16\pi^3} \psi(x,\vec{k})^2 $$

So, I had a huge question: how to use Mathematica to do integral $ \int d^2\vec{k} $?

Can anyone help me with this? Thanks!

POSTED BY: Jurandi Leao
3 Replies
Posted 5 months ago

In the documentation https://reference.wolfram.com/language/ref/Integrate.html

in the Examples, Basic Examples, Scope, Nested Integrals, it shows

Compute the second antiderivative of a function

Integrate[a x^2+b x+c, x, x]//Expand

So try

Integrate[Ψ[x,k]^2/(16 Pi^3),k,k]
POSTED BY: Bill Nelson

If it were an iterated integral, I would somehow expect (dk)^2 instead of d^2 k. I wonder if the meaning is a double integral, with k a vector of dimension 2, although this would not explain the d^2 k.

POSTED BY: Gianluca Gorni
Posted 5 months ago

Yes, "k" is a vector...

POSTED BY: Jurandi Leao
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract