C. As a concrete example, consider a large 3D box with volume V and E. = 0. We may approximate the sum by an integral Zizi Ni = J+ n(E)p(E) dE and the 3D density of state is n(E) = 2m 3/2 217 2 VE. Show that the equation of state is naaB = nolaB + 93(eBM). NI Where n = = is the total particle density in the box, no = V 2 = eBu(1 - eBM) -1 is the condensate density, laB = h(2mmk T) 2 is the thermal de Broglie wavelength and 1 xn - 1 In (Z) = r(n) Jo z-1en-1 dx is the Bose function, and BEC occurs when the phase density no = nhaB reaches no = 93(1) ~ 2.612 ... (Comment: Equation of state is the relation between thermodynamical variables, u and T in this case.)