Quantum Physics: Fourier transform of a function

[Sennap]

Homework Statement

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

Homework Equations

(1) $$\tilde{f} (k) = \frac{1}{\sqrt{2 \pi}} \int{f (x) e^{-ikx} dx}$$
(2) $$\psi (x,0)=\int{\phi(k)e^{ikx}dk}$$ (might be needed)

The Attempt at a Solution

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

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

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

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

 

[vela]

You made an algebraic error: e^ae^-b ≠ e^a/b. Fix that and try again.