# 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 $$\left |{\psi}_{'}(x,t) \right |^{2}$$=$$\left |{\phi}_{'}(x) \right |^{2}$$

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