The paper by P. A. M. Dirac addresses the discrepancies between the quantum mechanics of point-charge electrons and experimental observations, particularly the "duplexity" phenomenon where the observed number of stationary states for an electron in an atom is twice the theoretical prediction. To resolve this, Dirac introduces a new Hamiltonian for a point-charge electron that satisfies both relativity and the general transformation theory of quantum mechanics. This Hamiltonian includes additional degrees of freedom, leading to a spinning electron model with a magnetic moment and a spin angular momentum. Dirac demonstrates that this model explains all duplexity phenomena without arbitrary assumptions, although it still requires further refinement. The paper also discusses the angular momentum integrals and energy levels for motion in a central field, showing that the total angular momentum is a constant of the motion, and the energy levels are consistent with experimental results.The paper by P. A. M. Dirac addresses the discrepancies between the quantum mechanics of point-charge electrons and experimental observations, particularly the "duplexity" phenomenon where the observed number of stationary states for an electron in an atom is twice the theoretical prediction. To resolve this, Dirac introduces a new Hamiltonian for a point-charge electron that satisfies both relativity and the general transformation theory of quantum mechanics. This Hamiltonian includes additional degrees of freedom, leading to a spinning electron model with a magnetic moment and a spin angular momentum. Dirac demonstrates that this model explains all duplexity phenomena without arbitrary assumptions, although it still requires further refinement. The paper also discusses the angular momentum integrals and energy levels for motion in a central field, showing that the total angular momentum is a constant of the motion, and the energy levels are consistent with experimental results.