Quantum statistical entropy of black hole

By using the method of quantum statistics, we derive the partition function of bosonic and fermionic field in various coordinates and obtain the integral expression of the entropy of a black hole. Then via the improved brick-wall method, membrane model, we obtain that if we choose proper parameter, the entropy of black hole is proportional to the area of horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. We offer a new simple and direct way of calculating the entropy of black holes in various coordinates.