## 7 Stern–Gerlach experiments

This short chapter is devoted to the basic results of a very important experiment that firmly established the existence of spin one-half for the electron. It also provides an interesting insight into the concept of measurement in quantum mechanics.

### 7.1 Experimental set-up and electron’s magnetic moment

Consider a beam of electrons traveling in the *x*-direction subjected to an inhomogeneous magnetic field, *B*_{z}, in the *z*-direction, and received on a detector on the opposite side. If the electron has a magnetic moment, *μ*, then its interaction energy will be − *μ* · **B**. The force on the electron due to the magnetic field will be given by

where *μ*_{z} is the projection of *μ* in the *z*-direction. We assume the maximum value of ...