Solution to 1996 Problem 97

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.

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