\,.  

 The extension to the general case of a particle with higher spin is straightforward in principle but finding the basis spin functions for arbitrary spin is nontrivial for directions other than the z-direction. The linear combinations are summed over all the allowed spin quantum numbers, in the z-direction: 

 : 

 and column matrices are indexed by the allowed spin quantum numbers: 

 :\Psi(\mathbf{r},t) = \begin{bmatrix} \Psi(\mathbf{r},t,s) \\ \Psi(\mathbf{r},t,s-1) \\ \vdots \\ \Psi(\mathbf{r},t,-(s-1)) \\ \Psi(\mathbf{r},t,-s) \\ \end{bmatrix}\,.