Suppose $\phi(x)$ is the real Klein-Gordon field, then the single-particle wave function $\psi(x)$ corresponding to a momentum $p$ is given by (QFT,Ryder) $$\psi(x)=<0|\phi(x)|p>$$ The calculated result is just as expected ($e^{-ipx}$). But is this by definition or it comes from somewhere else?