How to go from the first expression to the second

How to go from the first expression to the second

Postby Guest » Fri Jan 15, 2021 8:31 am

[tex]\int\limits_{0}^{\infty} e^{i\vec{k}(\vec{y}-\vec{x})}\vec{k}^{-2}d^3k[/tex] = [tex]\int\limits_{0}^{2\pi} d\varphi\int\limits_{-1}^{1} d cos\lambda \int\limits_{0}^{\infty} d|\vec{k}|e^{i cos\lambda|\vec{k}||\vec{x}-\vec{y}|}[/tex]
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Re: How to go from the first expression to the second

Postby HallsofIvy » Fri Jan 15, 2021 10:58 am

I have no idea what the first expression is saying! You appear to have a vector, [tex]\vec{k}[/tex] to a negative power. How are you defining a vector to a power?

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Re: How to go from the first expression to the second

Postby Guest » Sun Jan 17, 2021 9:25 am

[tex]\vec{k}^{-2}=1/\vec{k}^2[/tex]. And [tex]\vec{k}^2[/tex] is just the square of the norm of the vector. So it is just a number.
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