Quantum Mechanics problem: Determine the value of the constant

In summary, the conversation is about a problem that asks to use canonical quantization to prove a relation involving a sum operator and a constant, with the hint of considering the commutator [H,X],X]. The poster asks for hints and ways to prove it, specifically mentioning the connection to the identity. Another person asks what ##< E_0 \mid [H,X],X]] \mid E_0 >## is, and the original poster thanks them for the help and mentions they were able to figure it out.
  • #1
Ineedhelpimbadatphys
9
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.
 

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  • #2
Please, everyone, be respectful of poster asking for a hint about one specific aspect of this problem.
 
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  • #3
Ineedhelpimbadatphys said:
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
 
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  • #4
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.
 
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Likes vanhees71 and topsquark

1. What is the purpose of determining the value of the constant in Quantum Mechanics?

The value of the constant in Quantum Mechanics is essential in understanding the behavior of particles at a quantum level. It helps in predicting the probability of a particle's position and momentum, as well as its energy levels. It also plays a crucial role in various quantum equations and theories.

2. How is the value of the constant determined in Quantum Mechanics?

The value of the constant in Quantum Mechanics is determined through experimental measurements and observations. Scientists use sophisticated instruments and techniques to collect data and analyze it to determine the value of the constant. It is a continuous process of refinement and improvement as new technologies and methods are developed.

3. Can the value of the constant change over time?

No, the value of the constant in Quantum Mechanics is considered to be a fundamental and unchanging property of the universe. It is a universal constant that remains the same regardless of time, location, or other variables. However, our understanding and measurement of the constant may improve over time.

4. What are the implications of determining the value of the constant in Quantum Mechanics?

Determining the value of the constant in Quantum Mechanics has significant implications in various fields, including technology, chemistry, and physics. It allows us to develop new technologies, such as quantum computing, and understand the behavior of matter at a microscopic level. It also helps us make accurate predictions and advancements in fields like materials science and quantum mechanics.

5. Is the value of the constant the same in all quantum systems?

Yes, the value of the constant in Quantum Mechanics is the same in all quantum systems. It is a fundamental property of the universe and remains constant regardless of the system or particles being studied. However, the value may vary slightly depending on the units used for measurement.

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