Solve Ehrenfest's Theorem: Find Position Expectation Value

[majeka]

I have been asked to "find a solution to Ehrenfest's Theorem" (in this case for the expectation value of position, of a particle confined to a circle). What does this mean - what kind of answer should i find?

 

[suyver]

Did you even try Google?

http://people.ccmr.cornell.edu/~muchomas/8.04/Lecs/lec_TDSE/node6.html

http://farside.ph.utexas.edu/teaching/qm/fundamental/node32.html

http://www.yorku.ca/marko/ComPhys/Ehrenfest/Ehrenfest.html


Why don't you show what you understand about this, what you tried and where you got stuck? I don't mean to sound rude, but it seems to me that you're just looking for someone to do your homework for you...

 

[majeka]

Thankyou, I have searched many times on google and other search engines, and have found (as on the websites you have shown me) that

m*(d^2/dt^2)<x> = <F>

which is a result of the form that I am looking for. But instead of <x> I have <exp(I*theta)>, so a function of theta, as I am interested in a particle confined to a circle. I have not been able to find out whether or not I can still use this same equation (despite my <exp(I*theta)> not being a linear variable like <x>). Please understand my problems with this; I am not trying to get someone else to do my homework for me - if you have never found it hard to do your 'homework', then you are very lucky.

 

[spdf13]

I don't remember all the details, but I thought for a potential proportional to r^2, you should expect out the classical value for such quantities as force and energy. You might want to try finding the classical value of the force for a particle confined to a circle using classical lagrangian mechanics, I don't think its that hard, and compare this answer to the quantum ananlog. Just an idea.

 

[majeka]

thanks!

Thanks spdf13,
I've tried what you said and I think it has worked...
Cheers!