It is well known the wave function of a fermion changes sign under rotation by \(2\pi\). Has this been verified experimentally?

The wave fucntion of a fermion changes sign under \(2\pi\) rotation. For xample, under a rotation by an angle \(\alpha\) the spin wave function transforms as \[ \psi(x) \longrightarrow \exp\big(-i\alpha \hat{n}\cdot\sigma/2\big) \psi(x).\] It then follows that for \(\alpha=2\pi\) the wave function changes sign. An experiment to detect the change in sign has been performed and has been verified using neutron interferometer.

**Reference:**

S. A. Warner et al.,``Observation of the Phase Shift of a Neutron Due to Precession in a Magnetic Field'',

Phys. Rev. Lett. {\bf 35} (1975) 1053.This group has directly observed the reversal of sign of the wave function of a fermion produced by a precession or \(2\pi\) radians in magnetic field using a neutron interferometer.