Computing Momentum Expectation Value ??

[Widdekind]

If the "expectation value" for a quantum 'particle's' momentum is [math]< \vec{p} > = <\Psi | \hat{p} | \Psi >[/math]; and if the momentum operator is [math]\hat{p} \equiv -i \hbar \vec{ \nabla }[/math]; and if the wave function [math]\Psi[/math] is exclusively real (as in the Hydrogen 1S state); then what ensures that the expectation value <p> winds up being a real number ?

 

EDIT: I suppose you could always decompose the wave function, into the momentum basis, wherein each plane wave would contribute a real-valued-amount of momentum (??).