Degenerate Perturbation Theory

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SUMMARY

The discussion focuses on the application of the completeness relation in Degenerate Perturbation Theory, specifically addressing the transition from equation 658 to 661 in the context of quantum mechanics. The user questions whether the inner product involving the states |n,l''> can be eliminated by performing the outer product first. The conclusion emphasizes that removing the |n,l''> states leads to the expression , which simplifies to a scalar value, lambda. This highlights the importance of understanding the manipulation of quantum states in perturbation theory.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with perturbation theory concepts
  • Knowledge of completeness relations in quantum states
  • Ability to interpret dense mathematical notation
NEXT STEPS
  • Study the derivation of completeness relations in quantum mechanics
  • Learn about the implications of Degenerate Perturbation Theory
  • Explore the mathematical techniques for manipulating inner and outer products
  • Review examples of perturbation theory applications in quantum systems
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Students and researchers in quantum mechanics, particularly those studying perturbation theory and the mathematical foundations of quantum state manipulation.

xdrgnh
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http://farside.ph.utexas.edu/teaching/qm/lectures/node53.html

So I was reading this and I don't understand how he goes from 658 to 661 using the completeness relation. In 661 if you use the completeness relaton can you get rid of the I n,l''>s by doing the outer product and ignoring the inner product first? I mean if you get rid of I n,l''>s you get <n,l'I H_1 In,l1>which equals lamba etc.
 
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bump.
 
Too hard to read the dense notation, sorry.
 

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