2009-11 (Energy_Band-2)

# 2009-11 (Energy_Band-2) - Bloch Schrdinger h2 2 2m U r r =...

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Bloch 定理 表述：在周期场中，描述电子运动的 Schrödinger 方程为 () () () 2 2 2 Ur r E r m ψψ ⎡⎤ −∇ + = ⎢⎥ ⎣⎦ h 其中， U ( r ) = U ( r + R l ) 为周期性势场， R l = l 1 a 1 + l 2 a 2 + l 3 a 3 为格矢，方程的解为： ( ) ( ) i eu ψ = kk kr rr —— Bloch 函数 这里， u k ( r ) = u k ( r + R l ) 是以格矢 R l 为周期的周期函数。 ( ) ( ) i e = l l kR r+R r 推论：

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§ 6 晶体能带的对称性 一、 E n ( k ) 函数的对称性 我们在前面已经论述过，在 k 空间中能带具有如上的特 性，这样关于能带的计算和论述就可以限定在一个有限 区域内，通常做法是取以 k=0 为中心的 Wigner-Seitz 胞，即第一布里渊区内。 ) ( ) ( h n n G k E k E v v v + = 1. 2. ) ( ) ( k E k E n n v v α = α 为晶体所属点群的任一对称操作。

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2009-11 (Energy_Band-2) - Bloch Schrdinger h2 2 2m U r r =...

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