Superposition of two stationary state

Let us now consider the linear superposition of the two previous stationnary: states.
y(x,t) = C1(t) j 2(x) + C2(t) j2(x)
By manually changing C1 and C2 you can observe that when the two coefficient are in phase, the eigenfunctions interfere constructively on the left side while they interfere destructively on the right side, because j 1(x)+j2(x) takes greater values on the left side. The particle has a greater probability to be detected on the left side.

In contrast, when C1 and C2 are in opposition, the eigenfunctions interfere destructively on the left and constructively on the right, because j1(x)-j2(x) takes greater values on the right. The particle has a greater probability to be detected on the right side.

By starting the animation, you can observe that C1(t) and C2(t) are alternatively in phase and in opposition, which result in an oscillation of the average position at frequency w21=w2 -w1. The linear superposition of two stationary states of different energies is no longer a stationary state.