Struggling with one step to show quantum operator equality

In summary, the person is struggling with a calculation involving quantum operator equality, specifically a step where two infinite sums appear when they are only supposed to be working with one infinite sum and one finite sum. They believe it may be due to an index shift in the solution. They are looking for an explanation of where the second infinite sum comes from.
  • #1
troglodyte
Gold Member
31
22
Hello guys,

I struggle with one step in a calculation to show a quantum operator equality .It would be nice to get some help from you.The problematic step is red marked.I make a photo of my whiteboard activities.The main problem is the step where two infinite sums pops although I work permanently with one Infinite sum and one finite sum.In the solution there is a index shift before the last step.Maybe this is the reason why suddenly one more infinite sum pops out.It would be nice if you can explain to me from where this second infinite sum comes from .
Thank you
 
Last edited:
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  • #2
You forgot the picture...
 
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Likes troglodyte
  • #3
DrClaude said:
You forgot the picture...
Thank you for your reply.
I thought I wouldn't get any reply so I have deleted them to reduce server costs.
 

Related to Struggling with one step to show quantum operator equality

1. What is the concept of quantum operator equality?

Quantum operator equality refers to the relationship between two quantum operators, A and B, where A is equal to B if and only if they produce the same results when applied to the same state vector.

2. Why is it important to show quantum operator equality?

Showing quantum operator equality is important because it allows us to understand the behavior of quantum systems and make accurate predictions about their outcomes. It also helps us to develop new quantum algorithms and technologies.

3. How do you prove quantum operator equality?

To prove quantum operator equality, you must show that the two operators produce the same results when applied to the same state vector. This can be done by using mathematical techniques such as commutation relations, eigenvalue equations, and unitary transformations.

4. What are some challenges in demonstrating quantum operator equality?

One challenge in demonstrating quantum operator equality is the complexity of the mathematical calculations involved. Another challenge is the limited understanding of quantum mechanics and the lack of experimental techniques to directly measure the operators.

5. What are the implications of not being able to show quantum operator equality?

If quantum operator equality cannot be shown, it may indicate a fundamental flaw in our understanding of quantum mechanics. It could also limit our ability to accurately predict the behavior of quantum systems and hinder the development of new quantum technologies.

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