Numerical modeling of the multi-stage Stern–Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Schrödinger equation

Abstract

We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern–Gerlach (SG) experiment conducted by R. Frisch and E. Segrè. This experiment consists of two Stern–Gerlach apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch–Segrè experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schrödinger equation. Our simulation utilizes a branching condition to predict the collapse of electron spins, and the outcome agrees with the Frisch–Segrè experimental observation and supports CQD as a potential model for electron spin evolution and collapse.

Numerical modeling of the multi-stage Stern–Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Bloch equation

“…However, a closed-form approximation of CQD matches the experimental data with a high coefficient of determination without the use of fitting parameters [12]. The approximation models the dynamics by means of the Schrödinger equation coupled with the CQD concept; this approach has been corroborated numerically [26]. Here, we validate CQD by numerically solving the Bloch equation instead to estimate the fraction of spin flip in the Frisch-Segrè experiment and achieve a high coefficient of determination.…”

“…Our source code is posted online [45]. An alternative approach, to avoid the stiffness, approximates the nuclear Larmor frequency as a constant and accelerates the solution using a variable transformation [26].…”

“…The coefficient of determination for our numerical simulation is R 2 num = 0.945, an alternative numerical solution that approximates the interaction with the nuclear magnetic moment and performs a variable transformation to avoid stiffness [26] yield R alt = 0.950, and the closed-form analytical solution obtained in [12] gives R 2 ana = 0.962. The statistical errors associated with the numerical results are [14], the blue dashed line is the closed-form analytical solution from CQD [12], the gray squares show the numerical CQD solution solved via the Schrödinger equation [26], and the green crosses are the result from the numerical CQD solution obtained here.…”

“…Fraction of spin flip for the multi-stage Stern-Gerlach experiment by Frisch and Segrè. The red circles are the original experimental data[14], the blue dashed line is the closed-form analytical solution from CQD[12], the gray squares show the numerical CQD solution solved via the Schrödinger equation[26], and the green crosses are the result from the numerical CQD solution obtained here.…”

Quantum mechanical modeling of the multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè

“…This discrepancy indicates that either our understanding of the FS experiment is lacking or the standard theoretical model is insufficient. Recent studies have modeled the FS experiment using an alternative model called co-quantum mechanics [34][35][36] without resorting to free parameters. Despite the existence of several theories regarding the reduction of the wavefunction that could potentially address the observed mismatch [37][38][39][40][41], this study remains within the orthodox framework of the standard quantum theory and the Born postulate [3][4][5][6].…”