Derivations of Bloch (Majorana--Bloch) equation, von Neumann equation, and Schr\"odinger--Pauli equation

TL;DR

This paper derives key quantum equations, including the von Neumann and Schrödinger--Pauli equations, from classical physics equations, providing a mathematical bridge between classical and quantum descriptions of electron spin.

Contribution

It presents a novel derivation of quantum equations from classical Bloch equations, connecting classical and quantum frameworks.

Findings

Derivation of the von Neumann equation from classical Bloch equations

Derivation of the Schrödinger--Pauli equation in quantum and co-quantum frameworks

Clarification of the transition from classical to quantum descriptions

Abstract

The transition from classical physics to quantum mechanics has been mysterious. Here, we derive the space-independent von Neumann equation for electron spin mathematically from the classical Bloch or Majorana--Bloch equation, which is also derived. Subsequently, the space-independent Schr\"odinger--Pauli equation is derived in both the quantum mechanical and recently developed co-quantum dynamic frameworks.