  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.
