Confused????

All energy eigen states (stationary states) have the form ${\psi}(x,t) = {\phi}(x) e^{-i {\omega}t}$ , where ${\omega}$ is the angular frequency so that $\left |{\psi}(x,t) \right |^{2} = \left |{\phi}(x) \right |^{2}$ implying that probability is independent of time.

Let ${\psi}_{1}(x)$ and ${\psi}_{2}(x)$ be two non-degenerate states such that follow above condition ${\psi}_{1}(x,t) = {\phi}_{1}(x) e^{-i {\omega}_{1}t}$

${\psi}_{2}(x,t) = {\phi}_{2}(x) e^{-i {\omega}_{2}t}$

Let ${\psi}_{'}(x,t)$ = ${\psi}_{1}(x,t)$ + ${\psi}_{2}(x,t)$

Question: Is the wave function ${\psi}_{'}(x)$ a stationary state. Meaning is $\left |{\psi}_{'}(x,t) \right |^{2}$ = $\left |{\phi}_{'}(x) \right |^{2}$