- #1
Lindsayyyy
- 219
- 0
Hi everybody
I showed the following:
[tex] \frac{1}{\hbar i} [H,xp]=x \frac {dV}{dx} - \frac {p^2}{m}[/tex]
Now I want to use this to show that:
[tex] \langle \frac {p^2}{2m} \rangle = \frac{1}{2} \langle x \frac {dV}{dx}\rangle[/tex]
whereas |E> is an eigenstate to H with the eigenvalue E. H x and p are operators. Furthermore in my 2nd equation the <> are the expectation value.
Can anyone help me with this? I'm learning for my final exams and I found this task in an old exam. I tried to solve <E|H|E> but that didn't lead me anywhere near it.
Thanks for your help
Homework Statement
I showed the following:
[tex] \frac{1}{\hbar i} [H,xp]=x \frac {dV}{dx} - \frac {p^2}{m}[/tex]
Now I want to use this to show that:
[tex] \langle \frac {p^2}{2m} \rangle = \frac{1}{2} \langle x \frac {dV}{dx}\rangle[/tex]
whereas |E> is an eigenstate to H with the eigenvalue E. H x and p are operators. Furthermore in my 2nd equation the <> are the expectation value.
Homework Equations
The Attempt at a Solution
Can anyone help me with this? I'm learning for my final exams and I found this task in an old exam. I tried to solve <E|H|E> but that didn't lead me anywhere near it.
Thanks for your help