Degenerate Perturbation Theory

In summary, Degenerate Perturbation Theory is a mathematical framework used to approximate the behavior of quantum systems with multiple energy levels that are close in value. It is used when the energy levels are nearly degenerate, which can occur due to symmetries or multiple interacting particles. This theory differs from regular Perturbation Theory in that it requires more complex calculations and techniques such as degenerate orthonormalization. Its limitations include only being applicable to nearly degenerate systems, assuming small perturbations and time-independence, and potentially inaccurate predictions for systems with large perturbations or strong interactions. Applications of Degenerate Perturbation Theory include studying atoms, molecules, solid-state materials, and particles in fields such as nuclear and particle physics.
  • #1
xdrgnh
417
0
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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  • #2
bump.
 
  • #3
Too hard to read the dense notation, sorry.
 

Related to Degenerate Perturbation Theory

1. What is Degenerate Perturbation Theory?

Degenerate Perturbation Theory is a mathematical framework used to approximate the behavior of quantum systems in which there are multiple energy levels that are close in value. It allows for the calculation of energy corrections and probability amplitudes for transitions between these energy levels.

2. When is Degenerate Perturbation Theory used?

Degenerate Perturbation Theory is used when the energy levels of a quantum system are nearly degenerate, meaning they have similar values. This can occur when the system has symmetries or when there are multiple interacting particles.

3. How does Degenerate Perturbation Theory differ from regular Perturbation Theory?

In regular Perturbation Theory, the energy levels of a system are well-separated, allowing for a straightforward calculation of energy corrections. In Degenerate Perturbation Theory, however, the energy levels are close in value, making the calculations more complex and requiring the use of mathematical techniques such as degenerate orthonormalization.

4. What are the limitations of Degenerate Perturbation Theory?

Degenerate Perturbation Theory is only applicable to systems with nearly degenerate energy levels. It also assumes that the perturbation is small and that the system is time-independent. Additionally, it may not accurately predict the behavior of systems with large perturbations or strong interactions.

5. What are the applications of Degenerate Perturbation Theory?

Degenerate Perturbation Theory is commonly used in quantum mechanics to study systems such as atoms, molecules, and solid-state materials. It is also used in fields such as nuclear physics and particle physics to analyze the behavior of quantum particles and their interactions.

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