Neutron resonance spin-echo (NRSE) phenomena are investigated experimentall
y and theoretically. In our experiments, spin precession produced in a clas
sical manner and by neutron resonance is combined as two arms of a spin-ech
o machine. A magnetic-field scan in the classical SE coil reveals a spin-ec
ho signal of the precession produced by the NRSE arm. The neutron spin-flip
probability rho in the resonance coils turns out to be a key parameter of
the NRSE arm. The limiting cases rho =0 and rho =1 lead, respectively, to L
armor precession with phase phi (1) in the static magnetic fields of the NR
flippers or to NRSE precession with phi (2). The case 0<<rho><1 produces q
uantum interference resulting in additional echoes with phases <phi>(3) = (
phi (1) + phi (2))/2 and phi (4) = +/- (phi (1) - phi (2))/2 The amplitude
of each pattern depends on the spin-flip probability rho and the initial po
larization. These experiments demonstrate explicitly the quantum-mechanical
principle of linear spin state superposition of neutron particle waves, an
d the interference as a result of that.