证明:b=2n-2一 a1·(a,2×a 倒格子的另一种定义 b2=2兀 ·(a2×a 3=2z、 a2×a b1口a2,b1a3=今b1=c2xa b=c1(a2×a2)=2z 2丌 2 丌(a2×a a1·(a2×a 同理(练习)b2 2xz(3×a1) 2z(a3×a1) a1·(a,xa d1·(a2×d3)( ) 2 1 2 3 2 3 1 a a a a a b       ⋅ × × = π ( ) 2 1 2 3 3 1 2 a a a a a b       ⋅ × × = π ( ) 2 1 2 3 1 2 3 a a a a a b       ⋅ × × = π 证明： 倒格子的另一种定义 1 2 1 ⊥ 3 b ⊥ a ,b a     1 2 3 b ca a    = × a1 ⋅b1 = ca1 ⋅(a2 × a3 ) = 2π      ( ) 2 1 2 3 a a a c    ⋅ × = π ( ) 2 ( ) 1 2 3 2 3 1 a a a a a b       ⋅ × × = π ( ) 2 ( ) 1 2 3 3 1 2 a a a a a b       ⋅ × × = π ( ) 2 ( ) 1 2 3 3 1 2 a a a a a b       ⋅ × × = π 同理(练习)