Wave packet width given a wave function

[Safder Aree]

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.

 

[DrClaude]

I don't understand why you have an integral there. You should be able to find an analytical form for Ψ.

 

[Safder Aree]

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?