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About integration of solid angle

  1. Feb 1, 2009 #1

    KFC

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    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.
     
  2. jcsd
  3. Feb 1, 2009 #2
    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].
     
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