Using the quantum statistical method, we directly obtain the partition function of Bose field and Fermi field on the background of Schwarzschild spacetime. The integral expression is obtained. According to the latest research results, Hawking radiation process of the black hole is a tunnel effect. During the creation of tunnel effect, the energy of the black hole changes. The lower limit of integral is the location of the black hole horizon. Therefore, the leading term of the black hole entropy is a quarter of the horizon area. In our calculation, there are no cutoffs. We obtain that the energy of the black hole radiation particle is proportional to the radiation temperature. This provides an insight into the thermodynamics and quantum property of the black hole.
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