# Fermions and Bosons

In analogy with orbital angular momentum, you can assume that *m* (the *z*-axis component of spin) can take the values –*s*, –*s* + 1, ..., *s* – 1, and *s*, where *s* is the total spin quantum number. For electrons, physicists Otto Stern and Walther Gerlach observed two spots, so you have 2*s* + 1 = 2, which means that *s* = 1/2. And therefore, *m* can be +1/2 or –1/2. So here are the possible eigenstates for electrons in terms of spin:

So do all subatomic particles have *s* = 1/2? Nope. Here are their options:

**Fermions.**In physics, particles with half-integer spin are called*fermions*. They include electrons, protons, neutrons, and so on, even quarks. For example, electrons, protons, and neutrons have spin*s*= 1/2, and delta particles have*s*= 3/2.**Bosons.**Particles with integer spin are called*bosons*. They include photons, pi mesons, and so on; even the postulated particles involved with the force of gravity,*gravitons*, are supposed to have integer spin. For example, pi mesons have spin*s*= 0, photons have*s*= 1, and so forth.

So for electrons, the spin eigenstates are

For photons, the eigenstates are |1, 1 >, |1, 0 >, and |1, –1 >.

Therefore, the possible eigenstates depend on the particle you’re working with.