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Multi-stage Stern$\unicode{x2013}$Gerlach experiments provide cascadedquantum measurements. The multi-stage Stern$\unicode{x2013}$Gerlach experimentconducted by Frisch and Segr\`e has been modeled analytically using quantummechanics by Majorana and revised by Rabi by including the hyperfineinteraction. However, the theoretical predictions do not match the experimentalobservation well. Here, we numerically solve the standard quantum mechanicalmodel, via the von Neumann equation, that includes the hyperfine interactionfor the time evolution of the spin. Thus far, the coefficients of determinationfrom the standard quantum mechanical model without using free parameters arestill below zero, indicating a mismatch between theory and experiment.Non-standard variants that improve the match are explored for discussion.

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