This state describes the zero-point energy of the vacuum. It appears that this sum is divergent – in fact highly divergent, as putting in the density factor 8 π π v 2 d v c 3 V shows. The summation becomes approximately the integral: 4 π π h V c 3 ∫ ∫ v 3 d v for high values of v. It diverges proportional to v for large v.