What are examples of wavefunction that changes with time but the square of wavefunction is constant?
$\begingroup$
$\endgroup$
2
-
$\begingroup$ You would get this if only the phase changes. $\endgroup$– mmesser314Jan 14 at 1:55
-
2$\begingroup$ This sounds a bit like a homework question... $\endgroup$– TLDRJan 14 at 3:11
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
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,
$$H \psi = E \psi$$
