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Predicts fine structure.
Video 5. Dirac equation for the electron and hydrogen Hamiltonian by Barton Zwiebach (2019) Source. Uses perturbation theory to get to the relativistic corrections of fine structure! Part of MIT 8.06 Quantum Physics III, Spring 2018 by Barton Zwiebach
Video 6. How To Solve The Dirac Equation For The Hydrogen Atom | Relativistic Quantum Mechanics by Dietterich Labs (2018) Source.