Solution
= Solution
The <Time-dependent Schrödinger equation> is
$$
\boxed{i\hbar\partial_t\Psi=-\frac{\hbar^2}{2m}\partial_x^2\Psi+V(x)\Psi.}
$$
A <stationary state> of <energy> $E$ has a <wavefunction> $\Psi(x,t)=\psi(x)e^{-iEt/\hbar}$, where
$$
-\frac{\hbar^2}{2m}\psi''+V\psi=E\psi.
$$
Its time dependence is only a <global phase>, and its <probability density> is independent of time.