Hi All.

Edited to allow for html.

a is the expectation of x, and b is the expectation of p in the initial 'dynamical state '

I know we dont normally do homework as a policy, but this has me stumped.

" Let a and b be the expectation values of x and its conjugate momentum p for a system in the dynamical state Phi(x). Show that the mean values of x and p vanish for the dynamical state

phi(x)=exp{(-i/hbar)*b*x}Phi(x+a) "

Yes theres two Phi's, a big one and a lil one.

Now... when i take the expectation of the new eqn, the exponential will drop out when i take the conjugates, which is good. Does the word dynamical tell me anything aobut the wavefunction of Phi? realness? Gaussian?

I cant take it any further after dropping out the exp's.

The fact that Phi is a function of x + a is throwing me too. Any help would be greatly appreciated.


Cheers.

Tulip.

your notation is very confusing to me. i am not familiar with the term "dynamical state", but i am going to assume that it means "not stationary state". perhaps it means "coherent state"?

the state you list is odd, it seems to have no spatial dependence nor time dependence.

And they expect me to answer it in 3rd year quantum :)

I assumed it meant we're not in a specific eigenstate/stationary state.

oh, the html has taken out part of my question!

The top post is displaying what i wanted now :)

Any help is much appreciated.

OK, now it is all clear. now i think that the word dynamic has no meaning in this context.

this statement that they want you to prove is true for any state. if you shift the argument of the wavefunction, the expectation value of position shifts. if you multiply by phase, the momentum shifts.

so you know how to take an expectation value, right?

&lang;<i>x</i>&rang;=&int;&phi;*(<i>x</i>)X&phi;(<i>x</i>)d<i>x</i>=&int;&Phi;*(<i>x</i>+<i>a</i>)<i>x</i>&Phi;(<i>x</i>+<i>a</i>)d<i>x</i>

since the exponentials cancel. now change variables, and you should be in business.

the momentum calculation procedes somewhat similarly. give it a try, and if you still can't get it, come back

Thanks.

I got the first one out an hour or so ago, had to assume normalised stuff tho - ie: (Phi(x+a))^2 = 1.

Ill get into the momentum one again, soon. I hit a snag last time - probably mucked up my working.

Got it all out.

I was stuck onthe momentum one when you get a -ihbar d/dx that you have to realise is the p operator.