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Math Help - Integral over angles

  1. #1
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    Integral over angles

    How to calculate:

    I = \int_0^{4\pi} d\Omega \frac{exp(i \hat{n}\vec{a})}{1-(\hat{n}\vec{b})^2},

    where a and b are fixed vector, and n is a unit vector pointing in the Omega direction.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Heirot View Post
    How to calculate:

    I = \int_0^{4\pi} d\Omega \frac{exp(i \hat{n}\vec{a})}{1-(\hat{n}\vec{b})^2},

    where a and b are fixed vector, and n is a unit vector pointing in the Omega direction.
    In spherical coordinates d \Omega = sin( \theta )d \theta d \phi. But your integrand contains neither variable(?) So thus your integrand is constant with respect to both angles and can be taken outside of the integral.

    -Dan
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  3. #3
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    Actually, \hat{n}=(sin(\theta) cos(\phi), sin(\theta) sin(\phi), cos(\theta)).
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