00:01
So let's say we have a potential that is independent of time.
00:06
So that means, like, you know, of course, our partial derivative with respect to t is zero for this potential.
00:12
And so in this case, we want to show that the expectation value of x is independent of time.
00:17
So our hamiltonian then is going to be time independent, right? because it's going to be like negative h, well, let's write it, negative h bar squared over 2m times this, plus v of x right so this is going to be intermittent of time which means that we can write our wave function as like a spatial part we'll just call this phi times e to the minus i e t over h bar where e is like the eigenvalue of h right h acting on si is just going to equal e times so with this in mind, our expectation of our position operator is going to be our integral from, you know, like negative infinity to infinity or something like that, of si, psi star times x times si, integrated with respect to x.
01:16
Or we could do this over all volume in three -dimensional space.
01:19
Doesn't really matter.
01:20
It doesn't change the result...