(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [tex]\phi (k)[/tex] be the Fourier transform of the function [tex]\psi (x)[/tex]. Determine the Fourier transform of [tex]e^{iax} \psi (x)[/tex] and discuss the physical interpretation of this result.

2. Relevant equations

(1) [tex]\tilde{f} (k) = \frac{1}{\sqrt{2 \pi}} \int{f (x) e^{-ikx} dx}[/tex]

(2) [tex]\psi (x,0)=\int{\phi(k)e^{ikx}dk}[/tex] (might be needed)

3. The attempt at a solution

We know that: [tex]\phi (k) = \tilde{\psi} (x) = \frac{1}{\sqrt{2 \pi}} \int{\psi (x) e^{-ikx} dx}[/tex] (eq. 1)

I'll let [tex]\tilde{\phi_2} (k)[/tex] be the Fourier transform of [tex]e^{iax} \psi (x)[/tex]

[tex]\tilde{\phi_2} (k) = \frac{1}{\sqrt{2 \pi}} \int{\psi (x) e^{iax} e^{-ikx} dx} = \frac{e^{a/k}}{\sqrt{2 \pi}} \int{\psi (x) dx}[/tex]

Can I do anything more? How's the result interesting?

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# Homework Help: Quantum Physics: Fourier transform of a function

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