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Introduction

The electron, proton, as well as other particles, all have an intrinsic angular momentum, like a ball spinning on its own axis. If one measures the component of this angular momentum along any direction one finds ± h / 2. This intrinsic angular momentum is called spin 1/2 . Classically, a spinning distribution of charge will have a magnetic moment. Quantum mechanical spinning particles also have magnetic moments associated with their spins. 

In their experiment O. Stern and W. Gerlach measured the intrinsic spin angular momentum of silver atoms and found it to take only two discrete values, + h / 2 and - h / 2 commonly called "spin up" and "spin down". A schematic diagram of the Stern-Gerlach apparatus is shown on the right. The source emits a collimated beam of silver atoms directed between the poles of a magnet. The magnet produces an inhomogeneous field. As the atoms are neutral they do not experience a Lorentz force. However, due to their intrinsic magnetic moments the atoms are deflected by the inhomogeneous field. The field causes an actual separation in space of atoms with spin up and spin down. The following animation gives an impression of the motion of the silver atoms in a Stern-Gerlach device.

Silver atoms

The magnetic moment of a silver atom is that of the spin of an electron. The inhomogeneous magnetic field deflects atoms with spin up and spin down in different directions. The atom is neutral and therefore there is no Lorentz force acting on it. The animation shows a superposition of wave packets with spin up (blue) and spin down (green) moving in an inhomogeneous magnetic field perpendicular to the plane of motion. 

The field causes an actual separation in space of the spin up and spin down components of the initial wave packet. 

Ions

If the magnetic moment of an ion is electronic in origin, the inhomogeneous magnetic field separates ions with spin up from those with spin down. The effect of the Lorentz force is small due to the large ionic mass. 

Electrons

An electron beam passing through a Stern-Gerlach device does not separate into spin-up and spin-down components. The spreading of the electron wave packet washes out the separation effect due to the electron spin. For an inhomogeneous magnetic field of the form B = B₀ ( 0 , 0 , y ), the motion of the particle is in the xy - plane. The effect of the Lorentz force is masked by the spreading of the electron wave packet.

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