= Solution
For normalized amplitudes $c_n,c_{n'}$ and a time-independent <observable> $A$, the <Schrödinger equation> gives
$$
\langle A\rangle(t)=|c_n|^2A_{nn}+|c_{n'}|^2A_{n'n'}
+2\operatorname{Re}\left[c_n^*c_{n'}A_{nn'}e^{-i(n'-n)\omega t}\right].
$$
The interference term therefore has
$$
\boxed{T=\frac{2\pi}{|n-n'|\omega}}\qquad(n\ne n').
$$
This is the <period of two-state quantum interference>. If the off-diagonal <matrix element> or either amplitude vanishes, the <expectation value> is constant, so this is not its unique fundamental period. Equal <energies> likewise give no beat.
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