The probability current (density) is defined in the 1D case as

$\begin{align*}J(x,t) = \frac{i \hbar}{2 m}\left(\Psi \frac{\partial \Psi^*}{\partial x} - \Psi^*\frac{\partial \Psi}{\partial...$
$J(x,t)$ represents the rate at which probability is ``flowing" past the point $x$ . We plug in the given formula for $\psi$ to find that
$\begin{align*}J(x,t) &= \frac{i \hbar}{2 m}\left(\Psi \frac{\partial \Psi^*}{\partial x} - \Psi^*\frac{\partial \Psi}{\pa...$
Therefore, answer (E) is correct.

Solution to 1996 Problem 97