PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin
The Structure of Quantum Mechanics, Ch Spin one-half, SU(2) and two-level dynamics
Problem
In a neutron interferometer each neutron, in spin state ∣χ⟩, is split coherently into two paths of equal amplitude. On path I a magnetic field along a unit vector b^ turns the spin through the angle α=γnBL/v; path II has no field. Take the detected intensity to be proportional to R^(b^,α)∣χ⟩+∣χ⟩2, with no other phase difference between the paths. (a) Using the closed form of the spin rotation operator, show that the intensity is proportional to 1+cos(α/2) for every incoming spin state ∣χ⟩ and every field direction b^. (b) For neutrons with v=2200ms−1 and γn=1.83×108rads−1T−1, find the field integral BL at which the intensity first falls to zero, and the smallest nonzero BL at which it returns to its value at B=0.