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Published October 28, 2023 | Published
Journal Article Open

Numerical modeling of the multi-stage Stern–Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Schrödinger equation

  • 1. ROR icon California Institute of Technology


We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern–Gerlach (SG) experiment conducted by R. Frisch and E. Segrè. This experiment consists of two SG apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch–Segrè experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schrödinger equation. Our simulation utilizes a branching condition to predict the collapse of electron spins, and the outcome agrees with the Frisch–Segrè experimental observation and supports CQD as a potential model for electron spin evolution and collapse.

Copyright and License

© 2023 The Author(s). Published by IOP Publishing Ltd. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.


This project has been made possible in part by Grant No. 2020-225832 from the Chan Zuckerberg Initiative DAF, an advised fund of the Silicon Valley Community Foundation.


Z H, K T, and D G developed the simulations and analyzed the data. S K helped with the validation of the simulations. L V W conceived the concept and developed the theory as well as closely supervised the project. All authors contributed to writing the manuscript.

Code Availability

The custom source code written in Mathematica for this study is available in Appendix and online [18].

Conflict of Interest

The authors declare no competing interests.


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Additional details

October 2, 2023
October 2, 2023