The Schrödinger equation, as a postulate, is a corner stone in quantum mechanics. The transition from classical physics to quantum mechanics, however, remains a mystery. In classical electrodynamics, the motion of the magnetic dipole moment of an electron is governed by the Bloch equation. Majorana stated that both the classical and the quantum-mechanical treatments on spin flip of atoms moving in a magnetic quadrupole field require integration of the same differential equations. Surprisingly, Majorana wrote the “Bloch” equation fourteen years before Bloch published his eponymous equation. Here, the classical Bloch equation for electron spin is mathematically converted to the space-independent von Neumann equation for a pure state of a two-level spin system. Subsequently, the space-independent Schrödinger–Pauli equation is derived in both frameworks of quantum mechanics and recently developed co-quantum dynamics. Therefore, the inverse conversion is shown, and the two-way transitions for a pure state of electron spin between the classical Bloch equation and the space-independent Schrödinger–Pauli equation are established.
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