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[itex]|\psi(x_1,x_2,t)|^2=|\psi(x_2,x_1,t)|^2[/itex]

thus [itex]\psi(x_1,x_2,t)=e^{i\phi}\psi(x_2,x_1,t)[/itex]

also [itex]\psi(x_2,x_1,t)=e^{i\phi}\psi(x_1,x_2,t)[/itex]

that means [itex]e^{2i\phi}=1[/itex] or [itex]e^{i\phi}=\pm 1[/itex]

For fermions

[itex]\psi(x_2,x_1,t)=-\psi(x_1,x_2,t)[/itex]

**Why does it happen to be different when we just switch the position of these particles?**