The standard eigenfunctions of orbital angular momentum are the so
called spherical harmonics
of chapter 4.2.
They show that the square orbital angular momentum has the possible
values
Further, the orbital angular momentum in any arbitrarily chosen
direction, taken as the -direction from now on, comes in multiples
of Planck's constant :
The possible values of the square spin angular momentum can be
written as
spin azimuthal quantum numberis usually called the
spinfor short. Note that while the orbital azimuthal quantum number had to be an integer, the spin can be half integer. But one important conclusion of this chapter will be that the spin cannot be anything more. A particle with, say, spin cannot not exist according to the theory.
For the spin angular momentum in the -direction
Particles with half-integer spin are called fermions. That includes electrons, as well as protons and neutrons and their constituent quarks. All of these critically important particles have spin . (Excited proton and neutron states can have spin .) Particles with integer spin are bosons. That includes the particles that act as carriers of fundamental forces; the photons, intermediate vector bosons, gluons, and gravitons. All of these have spin 1, except the graviton which supposedly has spin 2.