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

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 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.

Quantum Physics (quant-ph); Atomic Physics (physics.atom-ph)

arXiv:2407.08025 [quant-ph]

(or arXiv:2407.08025v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2407.08025 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.