Bad Qubits — Learn Quantum by Doing

Multiple choice

The indistinguishability requirement for two identical particles states that any physical prediction must be unchanged when the particle labels are swapped, written

|\psi(x_a, x_b)|^2 = |\psi(x_b, x_a)|^2

. What does this condition constrain, and what does it leave free?

It forces the wavefunction $\psi$ itself to be exactly equal under exchange, with no phase allowed
It constrains the energy but places no condition on the probability density
It requires the wavefunction to change sign under every exchange
It constrains only the modulus squared (probability density) to be symmetric; the wavefunction itself may still pick up a phase under exchange