Trouble with Harmonic Oscillator Problems in Quantum Physics

[Tuneman]

I am having trouble with 2 problems about the harmonic oscilator.
I realize this isn't the homework section, however I feel that in my situation where time is limited, perhaps someone would be able to give me a certain amount of leeway.


First of all the question tells me to use the wave function for when n=1

So I have:
Wavefunction = A[1]*r^1/2 * e^-((r^2)/2)


where r= (mw/(hbar))^1/2 and A[1] is A sub 1.

I am wondering when I am multiplying this by the complex conjugate, is the complex conjugate going to have a e^+((r^2)/2). I don't think I am but for some reason, in a solution finding <x> which equals ](integral) psi* (times) x (times) psi] those exponential functions did not appear. So I was wondering how they canceled out when you calculate <x>

also it asks me to calculate <p>, which I know equals m*d<x>/dt. My question is, if my <x> does not depend on t, because the time dependent part of the equation was canceled out when solving for <x>, how can I find d<x>/dt?

Any help would be appreciated, I'm sure my questions or equations aren't too clear, so if you have any questions, I will try to clarify. Thank you.

 

[vanesch]

I am having trouble with 2 problems about the harmonic oscilator.
I realize this isn't the homework section, however I feel that in my situation where time is limited, perhaps someone would be able to give me a certain amount of leeway.


First of all the question tells me to use the wave function for when n=1

So I have:
Wavefunction = A[1]*r^1/2 * e^-((r^2)/2)


where r= (mw/(hbar))^1/2 and A[1] is A sub 1.

This doesn't make sense: I'm sure you are missing a space variable in "r".
That explains then too why you don't find your exponential anymore once you've integrated over it...

cheers,
Patrick.

PS: and this really belongs in the homework section...

 

[quantumdude]

Tuneman, please don't double post. One thread is enough for one question.