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I need to find the fourier transform of displaced airy function.The function is $ψ_n(ξ) = N_n \text{Ai}(ξ − ξ_n)$, where $ξ=x/x_0$, $x_0=(1/2)^{1/3}$, $ξ_n = (3\pi/2)(n − 1/4)^{2/3}$ and $N_n$ is normalization constant.

We need to find its fourier tranform in momentum basis. I need to plot that out on mathematica but didnt get the correct results I just need to confirm about the fourier transform am I taking it right?

I used the fourier shift theorem and found the answer as $ψ_n(p) = (N_nx_0/\sqrt{2\pi}) \exp[i((px_0)^3-(px_0ξ_n))]$, is it the correct fourier transform?

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