Abstract
In an effort to provide an alternative method to represent a quantum spin, a precise 3D nonlinear dynamics method is used. A two-sided torque function is created to mimic the unique behavior of the quantum spin. A full 3D representation of the magnetic field of a Stern–Gerlach device was used as in the original experiment. Furthermore, the temporarily driven nonlinear damped model exhibits chaos, but struggles to be consistent through azimuthal angles in reproducing the well known quantum spin statistics.
Highlights
Scientists have questioned how quantum spins evolve into one of two states [1,2,3]
The geometry used to describe the relationship between the unit quantum spin, μ, and the unit magnetic field, B, can be seen in figure 1, where the angle of separation is β, and the unit vector of magnetic torque rotation is represented as n
In the presence of a nonuniform magnetic field, once the spin has collapsed into the spin up or down state there will be a classical force that acts on the spin magnetic moment
Summary
Scientists have questioned how quantum spins evolve into one of two states [1,2,3]. In follow up on that suggestion, a 2D nonlinear semi-classical perturbation model was developed and the results relatively produced the correct statistical quantum expectations [6]. This model was limited to a magnetic field from a current loop, but here the model is expanded into 3D. In the presence of a nonuniform magnetic field, once the spin has collapsed into the spin up or down state there will be a classical force that acts on the spin magnetic moment. The force value can be either positive or negative depending on the direction of μz [7]
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