Say we a have a sum of spin up plane wave solutions to the Dirac equation which represent the wave-function of a localized spin-up electron which is 90% likely to be found within a distance R of the origin of a spherical coordinate system. Four complex numbers at each spacetime point are needed? Fix time and graph this function at the points θ=∏/2, r=R, and phi=∏/2, ∏, 3∏/2, 2∏, ??? 5∏/2, 3∏, 7∏/2, 4∏. Up is θ=0. Do we need to graph two rotations or one? If we advance a very small "distance" forward (or backward) in time do the complex numbers considered as 2 dimensional vectors rotate a little? Can the above function be considered some sort of higher dimensional surface? If so are there some sorts of topological "twists" to this function? Thanks for any help! Edit, the title of the thread should be "How to graph solutions to the Dirac equation, some complex numbers?" I reread the thread many times but not the title. Sorry.