The expectation value of momentum for real wavefunctions is zero in stationary states, such as energy eigenstates of bound systems like the infinite square well. This is due to the momentum operator introducing an imaginary unit (i) in the integral, which cannot be canceled out by any other imaginary unit in real wavefunctions. However, in non-stationary states, represented as linear combinations of energy eigenstates, the expectation value of momentum can be non-zero, as demonstrated by the wavefunction $$\Psi(x,t) = \frac{1}{\sqrt{2}} \left[ \psi_1(x)e^{-iE_1 t / \hbar} + \psi_2(x)e^{-iE_2 t / \hbar} \right].
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