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I'm given $\Psi(x,t)$ as a proposal for a wave function. $\Psi(x,t)=\int_{1}^{1+\Delta k} e^{i(kx-wt)} k^2 dk$

Now I try to compute $\Psi^*(x,t)\Psi(x,t)$ wich is the product

$(\int_{1}^{1+\Delta k} e^{-i(kx-wt)} k^2 dk) (\int_{1}^{1+\Delta k} e^{i(kx-wt)}k^2 dk)$

In wich way should I transform this to a double integral? Taking into account that $w=w(|k|)$

Thanks for your time.

  • 0
    There is no comment about $\Delta k$ so I assumed is a real number because $k$ is.2011-09-25
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    This is a product of Fourier integrals, so you can obtain its Fourier transform as the convolution of the two Fourier transforms.2011-09-25
  • 0
    In Fourier Transforms, as far as I know, the range of integration is $\mathbb{R}$ not just $(1,1+\Delta k)$2011-09-25

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