About integration of solid angle

  • Thread starter KFC
  • Start date
  • #1
KFC
488
4

Main Question or Discussion Point

I am reading a book about integration on all possible momentum in 3D space, and it change the integration to a 1D integration and integration on solid angle, I don't know how does it happen

[tex]
\int d^3p \to \int p^2dp\int d\Omega
[/tex]

where [tex]\Omega[/tex] is the solid angle.
 

Answers and Replies

  • #2
534
1
Work in spherical coordinates [tex](p, \theta, \phi)[/tex], so that [tex]d^3 \vec p = p^2 \sin \theta \,dp \,d\theta \,d\phi[/tex], and note that the definition of solid angle is [tex]d\Omega = \sin \theta \,d\theta \,d\phi[/tex].
 

Related Threads on About integration of solid angle

Replies
2
Views
2K
  • Last Post
Replies
1
Views
882
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
14
Views
6K
Replies
8
Views
9K
Replies
1
Views
2K
Replies
1
Views
4K
  • Last Post
Replies
3
Views
517
Replies
6
Views
3K
  • Last Post
Replies
6
Views
823
Top