Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 4 / 6B / Solution

The Born rule and probability current in one dimension giveMultiply the Time-dependent Schrodinger equation by ${\Psi }^{\ast }$, subtract its complex conjugate multiplied by $\Psi$, and rearrange to obtain the continuity equation ${\rho }_t+j_x=0$.

For the stated superposition, the interference terms in $j$ are real and cancel from its imaginary part. Henceindependent of $x$ and $t$.