Certain quantum phenomena caused by fast periodic action on a neutron
beam are analyzed. In all cases when such an action affects the phase
or amplitude of a neutron wave, the arising neutron state is a superpo
sition of plane waves having a discrete energy spectrum and the corres
ponding wave numbers. In the case of phase modulation, the initial mon
oenergetic state can be reconstructed using another modulator. The pos
sibility of creating a neutron interferometer with spatially superpose
d beams that is based on this idea is considered. Some testing experim
ents are proposed.