关于第n布里渊区体积等于倒格子原胞体积的证明

The proof about the equation of volume of the n-th Brillouin zone and the volume of reciprocal's primitive cell

通过证明Wigner-Seitz原胞的体积等于原胞体积,说明第一布里渊区体积等于倒格子原胞体积;对于第n布里渊区和第n-1布里渊区建立保长同胚映射证明两者体积相等.

By proving the equation of the volume of Wigner-Seitz primitive cell and the volume of primitive cell,we conclude that the volume of the first Brillouin zone is identical to the volume of reciprocal＇ s primitive cell. We establish an isometric hemeomorphism mapping between the n-th and （ n - 1 ）-th Brillouin zone to prove the equation of their volume.