Weak field zeeman effect, why don't we still use degenerate perturbation theory?

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SUMMARY

The discussion centers on the application of degenerate perturbation theory in the context of the weak field Zeeman effect and spin-orbit coupling. It is established that the spin-orbit Hamiltonian only maintains degeneracy up to first order in perturbation theory, and higher-order corrections lead to a non-degenerate spectrum. The participants question whether relativistic corrections play a role in this context, particularly regarding the energy splitting caused by magnetic fields compared to spin-orbit interactions.

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  • Understanding of quantum mechanics principles, specifically perturbation theory.
  • Familiarity with spin-orbit coupling and its implications in quantum systems.
  • Knowledge of the Zeeman effect and its variations in weak and strong fields.
  • Basic grasp of relativistic corrections in quantum mechanics.
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  • Research the implications of spin-orbit coupling in quantum systems.
  • Study the differences between first-order and second-order perturbation theory.
  • Explore the weak field Zeeman effect and its mathematical formulations.
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Physicists, particularly those specializing in quantum mechanics, as well as students and researchers interested in the nuances of perturbation theory and its applications in atomic and molecular physics.

alemsalem
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the spin orbit coupling removes the degeneracy but not completely, should we still use the degenerate perturbation theory. is it because of relativistic corrections?

Thanks!
 
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Since nobody is answering I will say what I think the answer is although I'm not very sure, please correct me if I'm wrong.
the spin orbit Hamiltonian is only degenerate up to first order in perturbation theory, higher order ( or exact) energy eigenvalues will not give a non-degenerate spectrum.

I'm not sure about this answer because then the magnetic field energy splitting has to be smaller than the SECOND order splitting due to Spin orbit hamiltonian.

I hope I'm making sense.
 

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