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# DYK-05 Change in Sign of Fermion Wave Function under 2$\pi$ Rotation

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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.

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