Bad Qubits — Learn Quantum by Doing

Multiple choice

In the single-particle double-slit experiment, the probability of detecting a particle at a given position on the screen (both slits open) is given by

|\psi_1 + \psi_2|^2

, where

\psi_1

and

\psi_2

are the probability amplitudes for the two paths. What does this differ from, and why does it produce interference?

It equals $|\psi_1|^2 + |\psi_2|^2$ exactly, since amplitudes always add as independent probabilities
It is the same as the classical sum of two single-slit patches, just measured more precisely
It differs only because the particles physically collide with one another inside the apparatus
It differs from $|\psi_1|^2 + |\psi_2|^2$ ; the extra cross-term $2\,\mathrm{Re}(\psi_1^* \psi_2)$ is what creates bright and dark fringes