Derivations of Bloch (Majorana-Bloch) equation, von Neumann equation, and Schrödinger-Pauli equation

The transition from classical physics to quantum mechanics remains mysterious. In classical electrodynamics, the electron's magnetic dipole moment is described by the Bloch equation. Notably, Majorana formulated this equation 14 years before Bloch's 1946 publication, applying it to an atom, while Bloch considered it valid for only macroscopic magnetization. The author suggests renaming the Bloch equation to the Majorana-Bloch equation. Since neither Majorana nor Bloch, nor existing literature, provide a derivation, we offer our own using two models. We then mathematically convert the classical Bloch equation for electron spin to the space-independent von Neumann equation for a pure two-level spin system. Additionally, we derive the space-independent Schrödinger–Pauli equation within quantum mechanics and co-quantum dynamics frameworks. Thus, we establish the inverse conversion and the two-way transitions for a pure state of electron spin between the classical Bloch equation and the space-independent Schrödinger–Pauli equation.