# A Particle In An Infinite Box

1. Dec 13, 2008

### shlomo127

1. The problem statement, all variables and given/known data

A particle in an infinite box is in the first excited state (n=2).
Obtain the expectation value (1/2)*<x*p+p*x>

2. Relevant equations

3. The attempt at a solution
I'm completely baffled by this problem.
Can anyone just please point me in the right direction and then ill respond with what i get (because i know im gonna get stuck again)

Thanks!

2. Dec 14, 2008

### Coto

Hey shlomo. As a hint, the general formula for an expectation value is is given by:

$$<Q(x,p)> = \int_{-\infty}^{+\infty} \psi^* Q(x,p) \psi dx$$

where x, p are the position and momentum (quantum mechanical) operators.

This should hopefully give you a push in the right direction. As a first suggestion, you will have to find the wave equation $$\psi$$ for your specific situation.

3. Dec 14, 2008

### shlomo127

ok, im gonna work on that,
are there any websites you can recommend to help me learn this stuff?
my Prof doesn't explain anything well...
thanks!

4. Dec 14, 2008

### Coto

Well I suppose it's dependent on the situation you're in. What's the outline of the course?

Personally, I find it to be overwhelming if given a resource that goes into far more detail than the course requires.

5. Dec 15, 2008

### shlomo127

i beleive the wave equation is:
\psi(x) = Asin(kx) + Bcos(kx)
and k=sqrt((2mE)/(h-bar)^2)

so then the normalized wave function would be:
\psi n(x)=sqrt(2/L)*sin((n*pi*x)/L)

and the problem said that n=2.

And thats where I get stuck. Am i doing it right thus far? and how do i go further?

6. Dec 15, 2008

### soul

As far as I know so far you did right. My suggestion for the further is that you can calculate <xp> and <px> seperately ans sum them up. To do so, apply the operators with their usual orders and take their integral. I know, it seems a bit tidious but this is the only way that I think.

7. Dec 15, 2008

### shlomo127

ok, sounds good, can u set up on of the integrals so i can see how to do it?
then ill try to evaluate both integrals and ill post what i get.

Thanks!

8. Dec 15, 2008

### soul

For the p*x take the derivative of the x*wave function's conjugate and multiply it with the wave function itself and take the integral.

9. Dec 15, 2008

### EnershyMethod

Have you figured it out yet? I don't understand 'soul's last comment/step. I understand up to normalizing the wave function. I don't know how to derive px and xp.

Help!

10. Dec 15, 2008

### EnershyMethod

BUMP,
We need it for tomorrow.