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The improved Dirac equation is completely solved in the case of the hydrogen atom. A method of separation of variables in spherical coordinates is used. The angular functions are the same as with the linear Dirac equation: they account for the spin 1/2 of the electron. The existence of a probability density governs the radial equations. This gives all the quantum numbers required by spectroscopy, the true number of energy levels and the true levels obtained by Sommerfeld’s formula.

Resolution in the Case of the Hydrogen Atom of an Improved Dirac Equation