Quantum Mechanics problem: Determine the value of the constant

[Ineedhelpimbadatphys]

Homework Statement

The problem states work for word.

Using canonical quantization relation, prove that
sum operator ((E_n -E_0)) |< E_n | X | E_0 >|^2) = constant

Where E_0 is the energy corresponding to the eigenstate | E_0 >. Determine the value of the constant. Assume the hamiltonian had a general form H = P/2m +V(X)

Hint: One way to proof this is to think how [H, X], X] is connected to the obove identity.

Relevant Equations

all equations i have are in the statement.

I have no idea where to start with this problem. I am interested in any hints, or ways to proof this. But i would especially like to know how the commutator is connected to the identity.

 

[Nugatory]

Please, everyone, be respectful of poster asking for a hint about one specific aspect of this problem.

 

[topsquark]

Homework Statement:: The problem states work for word.

Using canonical quantization relation, prove that
sum operator ((E_n -E_0)) |< E_n | X | E_0 >|^2) = constant

Where E_0 is the energy corresponding to the eigenstate | E_0 >. Determine the value of the constant. Assume the hamiltonian had a general form H = P/2m +V(X)

Hint: One way to proof this is to think how [H, X], X] is connected to the obove identity.
Relevant Equations:: all equations i have are in the statement.

I have no idea where to start with this problem. I am interested in any hints, or ways to proof this. But i would especially like to know how the commutator is connected to the identity.

What is $< E_0 \mid [H,X],X]] \mid E_0 >$?

-Dan

 

[Ineedhelpimbadatphys]

Thank you so much. I did actually manage to figure it out. I had tried calculatibg that, and got stuck at < E_0 | XHX | E_n > and assumed I was wrong.

After seeing this, I just kept trying and got it. thank you.