- #1

Sennap

- 6

- 0

## Homework Statement

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.

## Homework 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)

## 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?

Last edited: