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

  • $\begingroup$ You would get this if only the phase changes. $\endgroup$
    – mmesser314
    Jan 14 at 1:55
  • 2
    $\begingroup$ This sounds a bit like a homework question... $\endgroup$
    – TLDR
    Jan 14 at 3:11

1 Answer 1


Energy eigenstates have this property. If a state is an energy eigenstate, then the time-dependent Schrödinger equation is

$$i \hbar \frac{\partial \psi}{\partial t} = H \psi $$ $$= E \psi$$

which is solved by

$$\psi(x,t) = \psi(x)e^{-itE/\hbar}$$

where $\psi(x)$ solves the time-independent Schrödinger equation,

$$H \psi = E \psi$$


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