A Numerical Experiment with the Stern-Gerlach Geometry

The Stern-Gerlach (SG) experiment reported in 1922 was an important milestone in the history of physics. The passing of a collimated neutral beam of silver atoms through a long, strong and asymmetrical magnet caused the atoms of silver out of a horizontal slit to split roughly into two separate beams forming a hollow lip figure (as seen on a plate held normal to the beam) instead of being a filled-in lip figure as suggested by some theoretical calculations. The SG results were thought to indicate that the observed phenomenon can not be explained using classical physics. Following a classical numerical approach by the author using a double-slit geometry, results are given for a 3D numerical SG type experiment showing clearly that a binary beam splitting is possible for certain conditions using an inverse square relation as the only source of forces- thus giving the possibility of a classical interpretation to the problem. For simplicity, we use what is mathematically equivalent- a dipole of charges to represent the magnetic dipole of the atom, and sets of fixed charges or potential surfaces around the path of the beam to represent the poles of a magnet. Although not exactly following the SG setup, the present results, nonetheless, are useful in showing the clear discrete behavior that can be caused by the combination of a fixed boundary, a strong field asymmetry and the highly nonlinear mapping of the inverse square law of forces coupled with the spin direction of a particle