What is the uncertainty of Δx for the given wavefunction?

[JonathanT]

Homework Statement

Suppose that at one instant in time the wavefunction of a particle is

ψ(x) = $\sqrt{b}$e^-b|x|

Estimate the uncertainty of Δx for this wavefunction.

Homework Equations

ΔxΔp ≥ h(bar)/2

h(bar) = h/2pi

The Attempt at a Solution

Do I just calculate the standard deviation of this function? My book doesn't really go into explaining how these values are related or even how to find the standard deviation of a function like this.

The only examples I'm given are simple examples where Δp is given or Δx is given and you calculate one or the other using algebra. Not sure what to do with this.

Part (a) of the problem was simply showing that ∫|ψ|² dx = 1 when evaluated from -∞ to ∞. That was simple enough. I'm just stuck here.

 

[JonathanT]

http://img811.imageshack.us/img811/3791/001sfe.jpg

There. I know you guys love seeing work. : ]

I feel like I'm just throwing math at this problem and not really thinking about what its even asking for. I'm grasping at strings here. Saw a few relations between Δx and standard deviation and then just calculated the standard deviation for this function. If this is the right answer I'll be surprised but its the best I've got now. Any input would be awesome.