  We consider a spherical symmetric black hole in the Schwarzschild metric and
apply Bohr-Sommerfeld quantization to determine the energy levels. The
canonical partition function is then computed and we show that the entropy
coincides with the Bekenstein-Hawking formula when the maximal number of states
for the black hole is the same as computed in loop quantum gravity, proving in
this case the existence of a semiclassical limit and obtaining an independent
derivation of the Barbero-Immirzi parameter.
