Proposed Differential Equation for Spin 1/2
  Intimate though the connection is between orbital angular momentum and intrinsic spin, there are differences between them the two quantities. One of them is the fact that while orbital angular momentum has a wave-mechanics description by courtesy of Legendre's equation, spin lacks one. In this paper, we show that there exists a differential eigenvalue equation whose solutions are the spin-1/2 eigenvectors. 
H. V. Mweene