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Published June 6, 2022 | Published
Journal Article Open

Derivation from Bloch Equation to von Neumann Equation to Schrödinger-Pauli Equation


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

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© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Received 09 July 2021. Accepted 08 May 2022. Published 06 June 2022. The author thanks Dr. Zhe He for discussing the manuscript and verifying the derivations and Prof. JT Shen for discussing the work. No funding was received for conducting this study. Contributions: NA (single author). Data Availability. All data used in this study are available from the author upon reasonable request. Code Availability. All custom codes used in this study are available from the author upon reasonable request. The authors have no relevant financial or non-financial interests to disclose. Humans and/or Animals Rights: NA (no human subjects/animals).

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