Struggling with one step to show quantum operator equality

Click For Summary
SUMMARY

The discussion focuses on a user's difficulty in demonstrating quantum operator equality, specifically regarding the emergence of a second infinite sum during calculations. The user mentions working with one infinite sum and one finite sum, but encounters confusion due to an index shift that introduces an additional infinite sum. The need for clarification on this step is emphasized, indicating a gap in understanding the manipulation of series in quantum mechanics.

PREREQUISITES
  • Understanding of quantum mechanics and operator theory
  • Familiarity with infinite series and summation techniques
  • Knowledge of index shifting in mathematical expressions
  • Basic skills in mathematical notation and problem-solving
NEXT STEPS
  • Study the concept of index shifting in summations
  • Explore the properties of infinite series in quantum mechanics
  • Learn about operator equality and its implications in quantum theory
  • Review examples of manipulating sums in quantum calculations
USEFUL FOR

Students and researchers in quantum mechanics, mathematicians dealing with series, and anyone interested in the mathematical foundations of quantum operator theory.

troglodyte
Gold Member
Messages
31
Reaction score
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:
Physics news on Phys.org
You forgot the picture...
 
  • Like
Likes   Reactions: troglodyte
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.
 

Similar threads

Undergrad Quantum Computing "Not" Operation - Mathematics Steps For Deriving It
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Understanding Operators in Matrix Mechanics
  • · Replies 1 ·
Replies
1
Views
2K
Finding Eigenvalues of an Operator with Infinite Basis
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Time evolution in quantum field theories
  • · Replies 79 ·
3
Replies
79
Views
19K
Using a Taylor expansion to prove equality
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Rigorous Quantum Field Theory.
  • · Replies 246 ·
9
Replies
246
Views
46K
Graduate What Is the Expansion Postulate in Quantum Mechanics?
  • · Replies 1 ·
Replies
1
Views
9K
MHB Probability and Operators in Quantum Mechanics
  • · Replies 1 ·
Replies
1
Views
3K
Ladder operators in quantum mechanics
  • · Replies 4 ·
Replies
4
Views
7K
Graduate Question about quantum statistical mechanics and thermodynamic arrow of time
  • · Replies 1 ·
Replies
1
Views
3K