  We show that an excellent approximation to the exact quantum solution of the
ground state of the Tavis-Cummings model is obtained by means of a
semi-classical projected state. This state has an analytical form in terms of
the model parameters and, in contrast to the exact quantum state, it allows for
an analytical calculation of the expectation values of field and matter
observables, entanglement entropy between field and matter, squeezing
parameter, and population probability distributions. The fidelity between this
projected state and the exact quantum ground state is very close to 1, except
for the region of classical phase transitions. We compare the analytical
results with those of the exact solution obtained through the direct
Hamiltonian diagonalization as a function of the atomic separation energy and
the matter-field coupling.
