# Examples when wavefunction is changing but probability density is constant?

What are examples of wavefunction that changes with time but the square of wavefunction is constant?

• You would get this if only the phase changes. Jan 14 at 1:55
• This sounds a bit like a homework question...
– TLDR
Jan 14 at 3:11

$$i \hbar \frac{\partial \psi}{\partial t} = H \psi$$ $$= E \psi$$
$$\psi(x,t) = \psi(x)e^{-itE/\hbar}$$
where $$\psi(x)$$ solves the time-independent Schrödinger equation,
$$H \psi = E \psi$$