- #1

Jennifer_ea

- 7

- 0

## Homework Statement

Any wavepacket can be obtained by the superposition of an inﬁnite number of plane waves using the so-called Fourier integral or Fourier transform

[itex]f(x,t) = \frac{1}{\sqrt{2\pi}} _{-\infty}\int^\infty A(k)e^{i(kx-\omega t)} dk[/itex]

Find at t=0 the representation of the wavepacket f(x) associated with the flat distribution given by:

A(k) =

0 for k<-K and k>K

[itex]\frac{1}{\sqrt{2K}}[/itex] for -K < k < K

## Homework Equations

The textbook I found that isn't leaving me entirely confused has replaced k with p (momentum), but that doesn't seem to be overly relevant to my lack of understanding. The one I've found that seem to be in the ball park is:

[itex]\left|A(p,t)^2\right| = \left|A(p)e^{\frac{ip^{2}t}{2mh-bar}}\right|^2 = \left| A(p,0) \right|^2[/itex]

## The Attempt at a Solution

I have figured out that A(k) is the Fourier transform, but after that I run into a brick wall. I can't even seem to get far enough to be able to make useful searches. I'm getting the impression that I need to do some more manipulation so that I can use the above equation, but right now it'd just be blind hammering without understanding why.

I feel like there may have a linking concept I'm not getting, even just a nudge in the right direction would be extremely helpful!