How Do You Calculate Xav, (X^2)av, and deltaX for a Simple Harmonic Oscillator?

[GreenLRan]

Homework Statement

Use the ground-state wave function of the simple harmonic oscillator to find: Xav, (X^2)av and deltaX. Use the normalization constant A= (m*omegao/(h_bar*pi))^1/4.

Homework Equations

deltaX=sqrt((X^2)av-(Xav)^2)

wavefunc=A*e^(-ax^2) ?

The Attempt at a Solution

I'm not sure if I'm on the right path, but I started out by plugging in A and doing the integral of the wavefunction. My question is... does doing this give me Xav? If not, how would I go about solving this problem?

 

[Dick]

If you plug the right A in and do the integral of $$\psi^* \psi$$ you should get 1. It's normalized. Getting <x>=Xav? requires inserting an x into the integral.

$$<f(x)>=\int \psi^*(x) f(x) \psi(x) dx$$

 

[Meir Achuz]

Of course, you know you need to use Psi^2.

 

[Dick]

Of course, you know you need to use Psi^2.

I said that in a pretty sloppy way. I've edited the post to clarify.