# Quantum Mechanics problem: Determine the value of the constant

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.

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

• topsquark, Lord Jestocost and berkeman
Gold Member
MHB
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

• vanhees71
• 