= Solution
Let the initial field be the normalized <coherent state> $|z\rangle=\sum_{n=0}^\infty c_n|n\rangle$, where $c_n=e^{-|z|^2/2}z^n/\sqrt{n!}$. The atom is again initially excited. Linearity of the <Schrödinger equation> gives
$$
\boxed{|\Psi(t)\rangle=\sum_{n=0}^\infty c_ne^{-i\omega(n+1/2)t}\left[\cos(g\sqrt{n+1}\,t)|e,n\rangle-i\sin(g\sqrt{n+1}\,t)|g,n+1\rangle\right].}
$$
The different <photon numbers> have different <Rabi frequencies>, so the state generally becomes entangled between atom and field. It cannot in general be replaced by one Rabi-oscillating atomic state multiplied by an unchanged <coherent state>.
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