Relativistic Hydrogen: Dirac vs Schrodinger, Fine Structure, Zitterbewegung

Relativistic Hydrogen: Dirac vs Schrodinger, Fine Structure, Zitterbewegung.

Figure 1. Hydrogen-like levels from the nonrelativistic Schrodinger equation against the exact Dirac-Coulomb spectrum: the relativistic levels are deeper and split by total angular momentum j (the fine structure, of order (Z alpha)^4), and a free Dirac packet trembles (Zitterbewegung) at angular frequency 2 m c^2 / hbar. Method: closed-form Schrodinger and exact Dirac (Sommerfeld) levels; deterministic.

nuclear charge Z50

packet momentum p (mc)0.60

WHAT TO TRY

Vary each control and watch the rail readouts respond.

Compare the diagnostic plot against the live scene.