The coherent superposition of particle quantum states resulting from differ
ent spatial paths shows well-known interference effects. Another type of in
terference is Larmor precession, which can be described as neutron wave int
erference in spin space, i.e. interference on the same spatial path. Here w
e show several new manifestations of interference phenomena of the latter t
ype. The interference is produced by coherent population of different I-z =
+/- 1/2 spin states in a polarized neutron beam between two resonant radio
-frequency (RF) spin flippers. Their spin hip probability, and thus the occ
upation numbers of the spin states, can be tuned between 0 and 1 by changin
g the RF amplitude. This leads to interference effects in the polarization
since the energy exchanged between the RF field and spin yields different p
hase evolution in the spatial parts of the neutron states. Depending on the
preparation of the initial neutron states, five values for the time-indepe
ndent phase difference between the final neutron states can be observed.