则本征矢 020-2 cos-e -i/2 SIn-e io/2 2 sIn-e iφ/ e iql2 - cos-e
则本征矢 i 2 i 2 cos e 2 sin e 2 − φ φ ⎛ ⎞ θ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ θ ⎜ ⎟ ⎝ ⎠ i 2 i 2 sin e 2 cos e 2− φ φ ⎛ ⎞ θ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ θ ⎜ ⎟ −⎝ ⎠
九 coS sInee 2 sin 0e ip -cos0 0-1/2 cos-e n 2 (1-cos 0)a,=sin Oe SIn-e i/2 SIn-e io/ n sine唧an1=(1+cos6)a2 cos-e iφ/2
( ) i n i cos sin e ˆS 2 sin e cos − φ φ ⎛ ⎞ θ θ = ⎜ ⎟ ⎝ ⎠ θ − θ h 2 Sn h = ( ) i 1 2 1 cos a sin e a − φ −θ=θ i 2 i 2 cos e 2 sin e 2 − φ φ ⎛ ⎞ θ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ θ ⎜ ⎟ ⎝ ⎠ ( ) i 1 2 sin e a 1 cos a φ θ =+ θ 2 Sn h = − i 2 i 2 sin e 2 cos e 2 − φ φ ⎛ ⎞ θ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ θ ⎜ ⎟ −⎝ ⎠
显然 s=(个)2(个+ 2 2|)2| +-a |4)=h个)(山)=个)
显然 ˆ S+ = h ↑ ↓ ˆ S+ ↓ = ↑ ↓↓ = ↑ h h z ˆ S 2 ↑ ↑ = ± ↓ ↓ h z ˆ S () 2 2 ⎛ ⎞ = +− ⎜ ⎟ ⎝ ↓ ⎠ ↑ ↑↓ h h ˆ S a + = ↑ ↓
s4|个)=九个)4个)=0 s=4)个 |)=h4)(个)=0 ↑)=剂(个个=h4
ˆ S 0 − ↓ = ↓ ↑↓ = h ˆ S − ↑ = ↓ ↑↑ = ↓ h h ˆ S − = h ↓ ↑ ˆ S 0 + ↑ = ↑ ↓↑ = h
.=2(7(4+)个 方(01 2(10 s2=2(个4) (0-i y2(i0
y ( ) ˆ S i 2 = − ↑ ↓ − ↓ ↑ h ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = i 0 0 i 2 S ) ˆ ( y h ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 1 0 0 1 2 S ) ˆ ( x h x ( ) ˆ S 2 = ↑ ↓ + ↓ ↑ h