Bloch（Majorana--Bloch）方程、von Neumann方程以及Schrödinger--Pauli方程的推导
Derivations of Bloch (Majorana--Bloch) equation, von Neumann equation, and Schrödinger--Pauli equation
AI总结：
该研究从经典Bloch（Majorana--Bloch）方程出发数学推导电子自旋的空间无关von Neumann方程，还在量子力学与共量子动力学框架下推导空间无关Schrödinger--Pauli方程，并在附录拓展了非线性von Neumann感应方程的形式。
摘要：
经典物理向量子力学的转变一直颇具神秘性。本文从经典Bloch方程（即Majorana--Bloch方程，本文也对其进行了推导）出发，通过数学方式推导出适用于电子自旋的空间无关von Neumann方程。随后，本文分别在量子力学框架与近期提出的共量子动力学（co-quantum dynamic，CQD）框架下，推导了空间无关Schrödinger--Pauli方程。附录部分将CQD符号分支函数纳入非线性von Neumann感应方程，推导了其显式双对易子形式与依赖态的有效哈密顿量形式。
英文摘要：
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 Schrödinger--Pauli equation is derived in both the quantum mechanical and recently developed co-quantum dynamic frameworks. An additional appendix incorporates the CQD signum branching function into the nonlinear von Neumann induction equation and develops its explicit double-commutator and state-dependent effective-Hamiltonian forms.
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