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Hydrogen Fine Structure

What you are seeing: the relativistic + spin-orbit fine-structure correction splits hydrogen levels by total angular momentum jj rather than orbital \ell. The 2s/2p degeneracy of Bohr lifts: 2p3/2_{3/2} moves up, 2s1/2_{1/2} and 2p1/2_{1/2} stay degenerate (Lamb shift is excluded here, see Lamb playground).

Figure 1. Hydrogen Bohr levels (cyan) split into FS multiplets (orange).
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WHAT TO TRY

  • Drag zoom n to expand a different principal level: the middle panel rebuilds its j-sublevels and the connector traces which Bohr level you are magnifying. n=1 has a single j (no splitting), n=2 splits into two rungs, n=3 into three.
  • Read the rungs: states with the same total j sit on one line (2S1/2 and 2P1/2 are degenerate), because the Dirac fine structure depends on n and j, not on the orbital l. That l-degeneracy is the deep result the splitting reveals.
  • Follow the bottom diagnostic: the splitting falls off as 1/n cubed, so the tightly packed high-n levels split far less than n=2. The level you are zooming is marked on the curve.