The behavior of a neutron as a quantum-mechanical top at the boundary
of two magnetically noncollinear media is analyzed. Attention is paid
to such phenomena as splitting of reflected and refracted beams, total
reflection 'forwards', cross interference, polarization and depolariz
ation effects. The exact formulae are obtained for the reflectivity an
d transmittance of neutrons with the spin precessing in the guide fiel
d. In a weak guide field approximation, they are simplified and genera
lized for a stratified, collinearly magnetized, medium and for oscilla
ting 'guide' fields. It is pointed out that reflection of neutrons can
be used to study the spin super-position and to carry out the Wigner
experiment on the result of a quantum mechanic measurement. Neutron sp
in turners including flippers can be made with mirrors on the basis of
magnetically anisotropic thin films.