If $$\psi(x)=A\exp(-x^2/a^2)\exp(ikx)$$ $\langle{p}\rangle=0$ since $\langle{x}\rangle=0$, since the integrand is an odd function and Ehrenfest theorem states $\frac{d\langle{x}\rangle}{dt}=\frac{\langle{p}\rangle}{m}$.
But explicit calculation of $\langle{p}\rangle= \int^{\infty}_{-\infty}\psi^*(x) \hat{p} \psi(x)dx$ and using $\hat{p}=-i\hbar \frac{\partial}{\partial{x}}$ gives $\hbar k$. I think Ehrenfest theorem is giving the wrong result because of the $ikx$ term,how to correctly use Ehrenfest theorem in this case?