Answer
The time-dependent wave function $\Psi(x, t)$ is given by
$\Psi(x, t)=\psi(x)e^{-i\omega t}$, where $\psi(x)=Ae^{ikx}+Be^{-ikx}$
Now,
$|\psi(x)|^2=\psi(x)\psi^*(x)$
or, $|\psi(x)|^2= \psi(x)e^{-i\omega t}\psi^*(x)e^{i\omega t}$
or, $|\psi(x)|^2=\Psi(x, t)\Psi^*(x, t)$
or, $|\psi(x)|^2=|\Psi(x, t)|^2$
Work Step by Step
The time-dependent wave function $\Psi(x, t)$ is given by
$\Psi(x, t)=\psi(x)e^{-i\omega t}$, where $\psi(x)=Ae^{ikx}+Be^{-ikx}$
Now,
$|\psi(x)|^2=\psi(x)\psi^*(x)$
or, $|\psi(x)|^2= \psi(x)e^{-i\omega t}\psi^*(x)e^{i\omega t}$
or, $|\psi(x)|^2=\Psi(x, t)\Psi^*(x, t)$
or, $|\psi(x)|^2=|\Psi(x, t)|^2$
