Today we know that if you make sequential Stern-Gerlach experiments, where the magnetic fields are at an angle $\alpha$, then the formula for the ratio how the beam splits is $$p_{1}=\cos^2 \bigg(\frac{\alpha}{2}\bigg)$$ for one side and $$p_{2}=1-p_{1}=\sin^2 \bigg(\frac{\alpha}{2}\bigg) $$ for the other side.

I understand this, but what I want to know is: Who discovered this formula?

I don't think Stern and Gerlach found it, because they don't mention it in their original paper, and I suspect it was already known by the time Pauli discovered his matrices, so it seems this formula was found sometime between 1922 and 1924, but in my research I cannot find any mention of who found it

If one of you could please give me a source where they talk about this development, I would be really thankful.

  • $\begingroup$ You suspect that it was already known by the time of Pauli? Have you check his papers? I think that the two-state quantum system might have been developed before but it is quick tricky to look for it. $\endgroup$
    – Mauricio
    Aug 28, 2023 at 17:13


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