Quantum Mechanics problem: Determine the value of the constant

  • #1
Ineedhelpimbadatphys
2
2
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.
 

Attachments

  • 385A8420-90F2-4204-8439-15C0224B4160.jpeg
    385A8420-90F2-4204-8439-15C0224B4160.jpeg
    25.8 KB · Views: 21

Answers and Replies

  • #2
Nugatory
Mentor
14,128
7,916
Please, everyone, be respectful of poster asking for a hint about one specific aspect of this problem.
 
  • Like
Likes topsquark, Lord Jestocost and berkeman
  • #3
topsquark
Science Advisor
Insights Author
Gold Member
MHB
1,804
741
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
 
  • #4
Ineedhelpimbadatphys
2
2
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.
 
  • Like
Likes vanhees71 and topsquark

Suggested for: Quantum Mechanics problem: Determine the value of the constant

Replies
1
Views
355
  • Last Post
Replies
4
Views
510
Replies
9
Views
660
Replies
12
Views
526
Replies
3
Views
572
Replies
8
Views
606
Replies
22
Views
833
  • Last Post
Replies
6
Views
592
Top