Integer versus half-integer angular momentum

The absence of half-integer orbital angular momentum states is established by considering the realizations of the angular momentum operators in spherical coordinates, theta and phi. The angular momentum raising and lowering operators switch the states between even and odd functions of theta-pi/2. Furthermore, the bottom and top states are both even. Hence there must be an odd number of states. This argument permits integer angular momenta and forbids half-integer angular momenta. (C) 2006 American Association of Physics Teachers.