Wave packet width given a wave function

  • #1

Homework Statement


Find the wave packet Ψ(x, t) if φ(k) = A for k0 − ∆k ≤ k ≤ k0 + ∆k and φ(k) = 0 for all other k. The system’s dispersion relation is ω = vk, where v is a constant. What is the wave packet’s width?

Homework Equations


[/B]
I solved for Ψ(x, t):

$$\Psi(x,t) = \frac{1}{\pi\sqrt{K_0+\Delta K}} \int_{-\infty}^{\infty} \frac{sin(k(k_0 + \Delta K))}{k} e^{i(kx-hk^2/2m)t}dk$$



The Attempt at a Solution



How would I go about finding the wave packet's width. I'm not even sure what this means. Thank you for any guidance.
 
Last edited:

Answers and Replies

  • #2
DrClaude
Mentor
7,554
3,894
I don't understand why you have an integral there. You should be able to find an analytical form for Ψ.
 
  • #3
I don't understand why you have an integral there. You should be able to find an analytical form for Ψ.
Am I supposed to be deriving the the wave equation from the dispersion equation?
 

Related Threads on Wave packet width given a wave function

  • Last Post
Replies
0
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
1
Views
1K
Replies
17
Views
349
  • Last Post
Replies
3
Views
646
  • Last Post
2
Replies
29
Views
212
Top