= Solution
Let $(a_1,a_2,a_3,a_4)=(0.1,0.4,0.3,0.86)$ and $S=0.9996$. For the time-independent well,
$$
\boxed{\psi(x,t)=\frac1{\sqrt S}\sum_{n=1}^4a_n\sqrt{\frac2L}\sin\!\left(\frac{n\pi x}{L}\right)e^{-icn^2t/\hbar},\quad0<x<L.}
$$
It remains zero outside the well. Each expansion coefficient acquires a phase of unit magnitude, so every <energy> <probability>, including the preceding $26.0\%$, is time-independent. The position <probability density> generally changes because cross terms between different energies oscillate.
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