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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 Bloch equation

  • 1. ROR icon California Institute of Technology


We numerically study the spin flip in the Frisch–Segrè experiment, the first multi-stage Stern–Gerlach experiment, within the context of the novel co-quantum dynamics (CQD) theory. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. The simulation shows that CQD closely reproduces, without using any fitting parameters, the experimental observations reported by Frisch and Segrè in 1933, which have so far lacked theoretical predictions.

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.


We would like to express our gratitude to the anonymous reviewers for their insightful comments and suggestions, which enhanced the clarity of our manuscript. This project has been made possible in part by Grant Number 2020-225 832 from the Chan Zuckerberg Initiative DAF, an advised fund of the Silicon Valley Community Foundation.

Data Availability

All data that support the findings of this study are included within the article (and any supplementary files).


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Additional details

October 2, 2023
October 2, 2023