Effective area of an antenna

We find the area of an isotropic linearly polarised antenna by statistical thermodynamics. A quantum-mechanical interpretation is given. For a matched antenna operating at reception, the number of photons captured in an electromagnetic wave is divided into two equal parts: one part is furnished to the load and the other part is reradiated. We prove, by the Heisenberg uncertainty principle, that the maximum effective area for any matched antenna is always greater than that of an isotropic antenna.