About integration of solid angle

[KFC]

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

$$\int d^3p \to \int p^2dp\int d\Omega$$

where $$\Omega$$ is the solid angle.

 

[adriank]

Work in spherical coordinates $$(p, \theta, \phi)$$, so that $$d^3 \vec p = p^2 \sin \theta \,dp \,d\theta \,d\phi$$, and note that the definition of solid angle is $$d\Omega = \sin \theta \,d\theta \,d\phi$$.