Is the Hydrogen Energy Level Formula Truly Degenerate in j?

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SUMMARY

The discussion centers on Griffiths' assertion regarding the hydrogen energy levels, specifically that while the formula for these levels incorporates fine structure and breaks degeneracy in the orbital quantum number l, it maintains degeneracy in the total angular momentum quantum number j. The confusion arises from the interpretation of degeneracy in j, as the energies depend on j according to Equation 6.67 in Griffiths' textbook. The key conclusion is that states with the same j can indeed have the same energy, despite variations in energy for states with different j values.

PREREQUISITES
  • Understanding of quantum mechanics, particularly angular momentum
  • Familiarity with Griffiths' "Introduction to Quantum Mechanics" textbook
  • Knowledge of fine structure in atomic physics
  • Basic grasp of quantum numbers and their significance in energy levels
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  • Review Griffiths' Equation 6.67 and its implications on energy levels
  • Study the concept of degeneracy in quantum systems
  • Explore the fine structure of hydrogen and its effect on energy levels
  • Investigate the relationship between quantum numbers l and j in atomic physics
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Students of quantum mechanics, physicists specializing in atomic theory, and educators seeking to clarify concepts related to hydrogen energy levels and degeneracy.

copernicus1
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Griffiths writes that the formula for the hydrogen energy levels taking fine structure into account "breaks the degeneracy in l" but "still preserves degeneracy in j." I'm confused by this, because the formula he gives (Eq. 6.67 in the textbook) depends on j. How can the system be degenerate in j if the energies depend on j?
 
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"The system is degenerate in j" = "different states with the same j have the same energy"
States with different j can have a different energy, even with the same l.
 

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