87.2.电子的自旋算符和自旋函数(不要求) 1671 由矩阵的厄密性:a12=a21,即:a21a21=a21a12=1 假设:a1=e,a为实数;a21=e- 即: 0 不失一般性,假设a=0,则 01 利用 10 01 0,=l(G-003)=i1(0 10 01 02 10 20 0 ● First●Prev●Next●Last● Go Back● Full Screen●cose●Quit• First • Prev • Next • Last • Go Back • Full Screen • Close • Quit §7.2. >fg^ŽÎÚg^¼ê(؇¦) 16/71 dÝ 5µa12 = a ∗ 21§=µa21a ∗ 21 = a21a12 = 1 bµa12 = e iα§α ¢ê¶a21 = e −iα =µ σbx = 0 e iα e −iα 0 ! , ؄5§bα = 0§Kµ σbx = 0 1 1 0! |^µσby = 1 2i ￾ σbzσbx − σbxσbz
σby = 1 2i ￾ σbzσbx − σbxσbz
= 1 2i ( 1 0 0 −1 ! 0 1 1 0! − 0 1 1 0! 1 0 0 −1 !) = 1 2i ( 0 1 −1 0! − 0 −1 1 0 !) = 1 2i 0 2 −2 0! = 0 −i i 0 !