Dirac's quantum theory of the electron addresses the discrepancy in the number of stationary states in atoms, where the observed number is twice that predicted by the original quantum mechanics. To resolve this, Goudsmit and Uhlenbeck proposed that electrons have spin angular momentum and a magnetic moment, a model later supported by Pauli and Darwin. Dirac showed that this model, when incorporated into the new quantum mechanics, explains hydrogen-like spectra accurately. The issue remains why nature chose this model over the point-charge model. Dirac's paper demonstrates that the previous theories were incomplete due to their inconsistency with relativity or quantum transformation theory. A relativistic Hamiltonian that satisfies both relativity and quantum transformation theory explains all duplexity phenomena without arbitrary assumptions. The spinning electron model is still a useful approximation, though its failure lies in the orbital angular momentum not being constant. In the absence of an electromagnetic field, Dirac derived a wave equation invariant under Lorentz transformations. This equation involved matrices representing spin and momentum, leading to a Hamiltonian with four components. These matrices satisfied specific anticommutation relations, allowing the wave equation to be invariant under Lorentz transformations. For an arbitrary electromagnetic field, Dirac extended the Hamiltonian to include scalar and vector potentials. This resulted in a wave equation with additional terms accounting for the electron's spin and magnetic moment. These terms, when divided by 2mc, represented the electron's magnetic moment, aligning with the spinning electron model. In a central field, Dirac analyzed the angular momentum integrals, showing that the total angular momentum, including spin, is a constant of motion. This led to the definition of a quantum number j, which takes integral values. The energy levels for motion in a central field were derived, showing that the theory accounts for the spin and relativistic effects, leading to energy levels consistent with experimental results. The theory matches the results of Pauli and Darwin, confirming the validity of the spinning electron model in explaining the observed phenomena.Dirac's quantum theory of the electron addresses the discrepancy in the number of stationary states in atoms, where the observed number is twice that predicted by the original quantum mechanics. To resolve this, Goudsmit and Uhlenbeck proposed that electrons have spin angular momentum and a magnetic moment, a model later supported by Pauli and Darwin. Dirac showed that this model, when incorporated into the new quantum mechanics, explains hydrogen-like spectra accurately. The issue remains why nature chose this model over the point-charge model. Dirac's paper demonstrates that the previous theories were incomplete due to their inconsistency with relativity or quantum transformation theory. A relativistic Hamiltonian that satisfies both relativity and quantum transformation theory explains all duplexity phenomena without arbitrary assumptions. The spinning electron model is still a useful approximation, though its failure lies in the orbital angular momentum not being constant. In the absence of an electromagnetic field, Dirac derived a wave equation invariant under Lorentz transformations. This equation involved matrices representing spin and momentum, leading to a Hamiltonian with four components. These matrices satisfied specific anticommutation relations, allowing the wave equation to be invariant under Lorentz transformations. For an arbitrary electromagnetic field, Dirac extended the Hamiltonian to include scalar and vector potentials. This resulted in a wave equation with additional terms accounting for the electron's spin and magnetic moment. These terms, when divided by 2mc, represented the electron's magnetic moment, aligning with the spinning electron model. In a central field, Dirac analyzed the angular momentum integrals, showing that the total angular momentum, including spin, is a constant of motion. This led to the definition of a quantum number j, which takes integral values. The energy levels for motion in a central field were derived, showing that the theory accounts for the spin and relativistic effects, leading to energy levels consistent with experimental results. The theory matches the results of Pauli and Darwin, confirming the validity of the spinning electron model in explaining the observed phenomena.