Quantum mechanical modeling of the multi-stage Stern$\unicode{x2013}$Gerlach experiment conducted by Frisch and Segr\`e

The multi-stage Stern$\unicode{x2013}$Gerlach experiment conducted by Frisch and Segr\`e includes two cascaded quantum measurements with a nonadiabatic flipper in between. The Frisch and Segr\`e experiment has been modeled analytically by Majorana without the nuclear effect and subsequently revised by Rabi with the hyperfine interaction. However, the theoretical predictions do not match the experimental observation accurately. Here, we numerically solve the standard quantum mechanical model, via the von Neumann equation, including the hyperfine interaction for the time evolution of the spin. Thus far, the coefficients of determination from the standard quantum mechanical model without using free parameters are still low, indicating a mismatch between the theory and the experiment. Non-standard variants that improve the match are explored for discussion.