Thread: Question about solution to the Dirac equation?

Is the wave function solution to the Dirac equation a function of space or momentum? I know the spinor part of solution is a function of momentum, so how could the overall solution be of just position. Is it a function of both or something, like psi(x,t;p), or something of that nature? I'm new to the Dirac equation.

A Dirac wave-function is a function of space and time, and there are many of them. For free particles the different solutions are labeled by the corresponding momentum. One says they are functions of x,t because the differential equation is a function of x and t. However, in using the wave-functions, you may usefully view them as functions of x, t, and p. It is convenient to view them this way precisely because of the dependence of the free spinor on p.