1. Reminder: Spin precession
Spin part of Hamiltonian:
Hspin = −µ·B = −γ S·B
γ = gq /2m (gyromagnetic ratio)
Acts on “spin space” only, so really:
Hspin = − γ Iwave fn  S·B
So we ignore spatial wave function
For B in z direction, say Hspin = ω0Sz
ω0 = γ B
Time-independent Hamiltonian, so solution is

2. Matrix Representation
If starting state is spin-left, i.e.
a0 = b0 = 1/√2,
then we get precession with period 2π/ω0:
NB after one period, overall sign reversed.

3. Neutron interferometry
ATOMINSTITUT Vienna
Beam split by Bragg diffraction in vertical crystal planes
Whole interferometer carved from a perfect crystal of silicon:
Separation between elements exact multiple of inter-atomic spacing.
Only ~ a dozen successfully made in 30 years!
Credit: NIST, Boulder, Colorado

4. 2π rotation (Warner et al 1975)
g factor of neutron = −3.83
i.e.  = ge/2mn even though no net charge!
Precession frequency ω0=−geB/2mn
de Broglie λ = nm
Effective ℓ ≈ 2.7 cm allowing for leakage of B outside magnet.
Time in field t = ℓ/v = ℓmnλ/h
Angle precessed: ω0t = −geBλℓ/2h
For 2π rotation we need B = 3.4 mT = 34 gauss
Observed period ≈ 62 G
4π rotation needed to restore original state: 2π rotation changes sign, as predicted by QM.