The Schrödinger eigenfunctions for the half-integral spins

In this paper we are interested in approaching the problem of the spin from a different point of view. We will show that the spin is neither basically relativistic nor quantum mechanical but reflects just a symmetry property related to the Lie algebra to which it is associated – a Lie algebra that may also be associated with the classical Poisson bracket. The classical approach will be compared with the usual quantum one to stress their formal similarities. With this “classical” representation of the spin by means of phase-space functions we proceed to the usual quantization procedure to derive a Schrödinger equation for the half-integral spin. We then solve this equation to obtain the half-integral spin eigenfunctions. The connection between this approach and that using the Heisenberg matrix calculus will also be worked out